he heights of adults in a certain town have a mean of 65.42 inches with a standard deviation of 2.32 inches. A random sample of 144 adults living in the center of the town was selected and their mean height was found to be 64.82 inches. Find the probability that a sample of this size would have a mean of 64.82 inches or less.

Answers

Answer 1

Answer:

0.001 = 0.1% probability that a sample of this size would have a mean of 64.82 inches or less.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, 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.

The heights of adults in a certain town have a mean of 65.42 inches with a standard deviation of 2.32 inches.

This means that [tex]\mu = 65.42, \sigma = 2.32[/tex]

Sample of 144:

This means that [tex]n = 144, s = \frac{2.32}{\sqrt{144}} = 0.1933[/tex]

Find the probability that a sample of this size would have a mean of 64.82 inches or less.

This is the pvalue of Z when X = 64.82. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{64.82 - 65.42}{0.1933}[/tex]

[tex]Z = -3.1[/tex]

[tex]Z = -3.1[/tex] has a pvalue of 0.001

0.001 = 0.1% probability that a sample of this size would have a mean of 64.82 inches or less.


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1) A- 95

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Step-by-step explanation:

1) 50 + 35+x = 180

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Step-by-step explanation:

[tex]1 \frac{4}{5} = \frac{9}{5}[/tex]

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Multiply the whole number by the denominator and add that to the numerator. I simplified [tex]-\frac{34}{10}[/tex] by dividing by two getting [tex]-\frac{17}{5}[/tex]. Then add [tex]\frac{9}{5}[/tex] and [tex]-\frac{17}{5}[/tex] together. Then put [tex]-\frac{8}{5}[/tex] into a mixed fraction. How many times does 5 go into 8 and what is the remainder? The answer is -1 times and the remainder is 3. The mixed fraction is [tex]-1 \frac{3}{5}[/tex].

The expression 1 4/10 + (-3 4/10 gives the value -1 3/5.

What are Mixed Fractions?

Mixed fractions are type of fractions which consist of a whole number part and a fractional part.

Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.

Given expression is,

1 4/5 + (-3 4/10)

Since a positive and negative combined, it becomes negative.

Also mixed fractions can be converted into improper fractions.

1 4/5 + (-3 4/10) = 1 4/5 - 3 4/10

                         = [(1 × 5 + 4) / 5] - [(3 × 10 + 4) / 10]

                         = (9 / 5) - (34 / 10)

Making the denominator of first fraction equal by multiplying with 2 on both numerator and denominator,

1 4/5 + (-3 4/10) = [(9 × 2) / (5 × 2)] - [34 / 10]

                         = (18 / 10) - (34 / 10)

                         = -16 / 10

                         = -1 6/10

                         = -1 3/5

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Answers

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Answer:

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Answers

Answer:

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Answers

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Step-by-step explanation:

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