Answer:
0.0918 = 9.18% probability that the mean pH measurement of these four specimens is greater than 8.2
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean 8 and standard deviation 0.3.
This means that [tex]\mu = 8, \sigma = 0.3[/tex]
Sample of 4:
This means that [tex]n = 4, s = \frac{0.3}{\sqrt{4}} = 0.15[/tex]
What is the probability that the mean pH measurement of these four specimens is greater than 8.2?
This is 1 subtracted by the pvalue of Z when X = 8.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.2 - 8}{0.15}[/tex]
[tex]Z = 1.33[/tex]
[tex]Z = 1.33[/tex] has a pvalue of 0.9082
1 - 0.9082 = 0.0918
0.0918 = 9.18% probability that the mean pH measurement of these four specimens is greater than 8.2
Which only lists multiples of 16? *
Mark only one oval.
1, 2, 4, 8, 16
16, 24, 32, 40
16, 32, 48, 64
Please help!
Which expression is equivalent to (1/2x+6)-(1/4x+2)?
A. 1/4 x - 4
B. 1/4 x + 4
C. 3/4 x - 4
D. 3/4 x + 4
Answer:
Choice B. 1/4 x + 4
Step-by-step explanation:
(1/2x+6)-(1/4x+2)
1/2x + 6 - 1/4x - 2
1/2 = 2/4
combine same values
1/4 x + 4
In a random sample of 42 Democrats from one city, 10 approved of the mayor's performance. In a random sample of 58 Republicans from the city, 12 approved of the mayor's performance. Find a 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance.
Answer:
The 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance is (-0.1078, 0.1702).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction of normal variables:
When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
In a random sample of 42 Democrats from one city, 10 approved of the mayor's performance.
This means that:
[tex]p_D = \frac{10}{42} = 0.2381, s_D = \sqrt{\frac{0.2381*(1-0.2381)}{42}} = 0.0657[/tex]
In a random sample of 58 Republicans from the city, 12 approved of the mayor's performance.
This means that:
[tex]p_R = \frac{12}{58} = 0.2069, s_R = \sqrt{\frac{0.2069*(1-0.2069)}{58}} = 0.0532[/tex]
Distribution of the difference:
[tex]p = p_D - p_R = 0.2381 - 0.2069 = 0.0312[/tex]
[tex]s = \sqrt{0.0657^2+0.0532^2} = 0.0845[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 1.645*0.0845 = 0.139[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.0312 - 0.139 = -0.1078
The upper end of the interval is the sample mean added to M. So it is 0.0312 + 0.139 = 0.1702
The 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance is (-0.1078, 0.1702).
Cameron runs 2.4 miles 3 days a week. How many miles does he run total in one week?
Answer:
5.6
Step-by-step explanation:
2.4 / 3 = x / 7
2.4 x 7 = 16.8
16.8 ÷ 3 = 5.6
Consider a taxi station where taxis and customers arrive in accordance with Poisson processes with respective rates of one and three per minute. A taxi will wait no matter how many other taxis are present. However, an arriving customer that does not find a taxi waiting leaves. Find the proportion of arriving customers that get taxis.
Answer:
The proportion of arriving customers that get taxis is:
= 33%.
Step-by-step explanation:
Rate of arrival of taxis = 1 per minute
In one hour, the number of taxis arriving = 60 (60/1)
Rate of arrival of customers = 3 per minute
In one hour, the number of customers arriving = 180 (60 * 3)
The proportion of arriving customers that get taxis = 60/180
= 0.333
= 33%
b) Since the taxis wait until they get a customer, it means that they will likely transport one out of 3 customers who arrive. Therefore, the proportion of arriving customers that get taxis is equal to 1/3 or 60/180, which is equal to 33%.
an item is regularly priced at 29. Joe bought it at a discount of 45% off the regular price.
Answer:
$13.05
Step-by-step explanation:
The prize will be $13.05 after the discount.
29x45%=13.05
OR
29x0.45=13.05
Gerri is working on a project that needs to be halfway completed by Friday. So far, she has completed of the project. How much of the project does she have to finish by Friday?
Answer:
So far Gerri is 1/3 complete and needs to be 1/2 complete by Friday. In order to find how much needs finished by Friday, we subtract the fractions.
1/2 - 1/3
1/2 + (-1/3)
3/6 + (-2/6)
(3+(-2))/6
1/6
Hope this helps
5. At Michael's store, a paint set is on sale for $39.99. The original price was
$66.65. What percent of the original price is the sale price?
PLS HURRY
around 50%
Step-by-step explanation:
because 30 of half of 60
Answer:
$ 26.66
Step-by-step explanation:
Minus the orignal price and the sale price and then you will get the answer
14/7 = n/21 what is the value of n
Answer:
n=42
Step-by-step explanation:
14/7=n/21
2=n/21
42=n
n=42
Answer:
n = 42
Step-by-step explanation:
14/7 = 2
42/21 = 2
Can someone please help me :(
Answer:
3 ^7
Step-by-step explanation:
7 goes in the box
you could do 5 + 2 and that is 7
Answer:
pretty sure you're supposed to put 7 in the box bc when multiplying numbers with exponents you add the exponents
Step-by-step explanation:
sorry if I'm mistaken
Use an inverse trig function to find the missing angle measure. Round your answer to the nearest tenth (first decimal place)
Answer:
x° ≈ 51.1°
Step-by-step explanation:
In this geometry, you are given the side opposite the angle, along with the hypotenuse. The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(x°) = 14/18
x° = arcsin(14/18) ≈ 51.0576°
x° ≈ 51.1°
Find the value of x. Round to the
nearest tenth.
What is the value of x when the Richter
scale rating is 4.37 Round your answer
to the nearest hundredth.
HELP this is due today!!!Use PEMDAS to evaluate the expression 7 x 6 + 8 − 16 ÷ 4. (4 points) 40 42 44 46
Answer:
46
Step-by-step explanation:
7 x 6 + 8 − 16 ÷ 4
42+8-16 ÷4
42+8-4
50-4
46
Answer:
46
Step-by-step explanation:
the answer is 46 may i be marked brainliest?
I will give the brainlist...plz help me.
Answer:
0.8,1.4
Step-by-step explanation:
0.8 is the biggest portion of the candy
A bag contains 5 blue marbles, 4 red marbles, and 3 orange marbles. You ask a friend to pick one without looking. What is the
probability that he picks one that is not red?
Answer:
8/125 (blue) +3 (orange) +4 (red) =12 (total)
5 (blue) +3 (orange)=8 (number of marbles that aren't red) or 12 (total) - 4 (red marbles)=8
or 66.6667%Which of the following statements are true about the function below? Select all that apply. f(x)=(x-4)^2-1
Answer:
the zero is at 4 (option 1)
and the minimum is -1 (option 2)
Step-by-step explanation:
the zero is at 4 (option 1)
and the minimum is -1 (option 2)
Jasmine has $4.90 in quarters, dimes, nickels, and pennies. She has 2 more dimes than
quarters. She has 3 more nickels than quarters. She has 4 more pennies than quarters. How
many quarters does Jasmine have? Note: A quarter is worth $0.25, a dime is worth $0.10, a
nickel is worth $0.05, and a penny is worth $0.01.
Answer:
11
Step-by-step explanation:
A loss of $13.50 on a washing machine represents 15% loss on the selling price. what is the selling price?
Answer:
$90
Step-by-step explanation:
Given data
Given data
Loss= $13.5
Percentage of the loss= 15%
Let the full loss be x
Hence we can find the value of x as
15/100*x= 13.5
0.15x= 13.5
divide both sides by x
x= 13.5/0.15
x= $90
Hence the loss in full is $90
Analyze the data represented in the graph and select the appropriate model. A) exponential B) linear C) none D) quadratic
Answer:
exponentialIt couldn’t be liner, liner is straight, the line is wriggly,, quadriceps obv no, so it has to be exponential.
Hi here equation everybody please help thanks
Answer: 2(3x+1)
Step-by-step explanation:
2(3x+1) ==> 2(3x)+2(1)
6x+2
Answer:
2(3x + 1)
Hope that helps! :)
Step-by-step explanation:
The diameter of a cake is 7.8 inches. What is the area of the cake?
Answer:
A = 12.25 sq inches
Step-by-step explanation:
A = (7.8/2)²π
A = 3.9²π
A = 12.25 sq inches
Given m∠3+m∠8=180° .
Answer:
5.175117
Step-by-step explanation:
What value is missing from the table
Answer:
C. $15.75
Step-by-step explanation:
If one costs $1.05, 15 would be:
15 (1.05) = 15.75
Answer:
15.75
Step-by-step explanation:
1.05 a gallon times 15 gallons is 15.75
The population of China was about 1.39 billion in the year 2013with an annual growth rate of about 0.6\% . Find an equation P(t) that represents the growth function for China. Write your answer in the form a * (b) ^ 2 in billions Provide your answer below:
Answer: 1.39(1.006)^t
Step-by-step explanation:
The equation P(t) that represents the growth function for China is P(t) = 1.39 * ( 1.006)ⁿ.
What is a Function ?A statement that relates two unknown parameters such that one is dependent on the other is called a function.
It is given that
Initial population = 1.39 billion in 2013
Growth Rate = 0.6%
Let a represent the initial population
b is the growth rate
and 2 be the elapsed year from 2013
and let the population at any given year is P(t)
Then the equation formed is
P(t) = a * bⁿ
P(t) = 1.39 * ( 1.006)ⁿ
Therefore the equation P(t) that represents the growth function for China is P(t) = 1.39 * ( 1.006)ⁿ.
To know more about Function
https://brainly.com/question/21145944
#SPJ2
PLEASE HELP FAST I WILL GIVE YOU BRAINLIEST
AABC - AQRS
Find the missing side length, n.
R
B.
12.5
5
2
А-
-C
4
10
n = [?]
Enter
Answer:
5
Step-by-step explanation:
yoy need to find hue multiplying factor, this is done by dividing one of the sides in QRS, by one in ABC. you can divide 10 by 4 to give you 2.5, and then multiply that by 2 to get 5
Solve for a side in right triangles
can u plz help me!? i need help
the answer is 4 buses
Step-by-step explanation:
because you multiply 30 times 4 and it gives you you the right answers
Determine the measure of the missing angle in the figure below.
DRAG & DROP THE ANSWER
90
45
75
Missing angle:
Answer:
Step-by-step explanation:
What is the volume of composite shape to the nearest whole number?
please help
Step-by-step explanation:
answer is 52
i hope this helps