The following are questions from a self-quiz.
According to some study, the height for Northern European adult males is normally distributed with an average of 181 centimeter and a standard deviation of 7.3 centimeter. Suppose such an adult male is randomly chosen. Let X be height of that person. The next 2 questions correspond to this information. The answer may be rounded up to 3 decimal places of the actual value.
a) The probability that the person is between 160 and 170 centimeters is
b) The probability that the person is higher than 190 centimeter is
Please state how you determined the probability from the standard normal table.

Answer:

0.0635 ; 0.1093

Step-by-step explanation:

Given that :

Mean (m) = 181

Standard deviation (s) = 7.3

Height = x

a) The probability that the person is between 160 and 170 centimeters

160 < x < 170

P(x < 160) - P(x< 170)

Z = (170 - 181) / 7.3) ; (160 - 181) / 7.3

Z = - 1.51 ; Z = - 2.88

P(Z < - 1.51) - P(Z < - 2.88)

0.0655 - 0.0020 (from Z table ; first integer of the y axis, decimal point value on the horizontal x axis ; the value at the intersection is the z probability value).

0.0655 - 0.0020 = 0.0635

b) The probability that the person is higher than 190 centimeter

P(x > 190)

Zscore = (x - m) / s

Zscore = (190 - 181) / 7.3

Zscore = 1.23

P(Z > 1.23) = 1 - P(Z < 1.23)

P(Z > 1.23) = 1 - 0.8907

P(Z > 1.23) = 0.1093

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