Question

The mean of a normally distributed data set is 110, and the standard deviation is 15.

a) Use the standard normal table to find the probability that a randomly-selected data value is greater than 95.

b) Use the standard normal table to find the probability that a randomly-selected data value is greater than 125.

Answer 1

From the standard normal table, the respective probabilities are; 0.908 and 0.841

How to find the probability from z-score?

Formula for calculating the standard score or z score is:

z = (x - μ)/σ

where:

z is the standard score

x is the raw score

μ is the population mean

σ is the population standard deviation

A) We are given;

x = 95

μ = 110

σ = 15

Thus;

z = (95 - 110)/15

z = 1.33

From the normal standard distribution table we can find the probability from the z-score as;

P(x > 95) = 1 - 0.091759.

P(x > 95) = 0.908

B) We are given;

x = 125

μ = 110

σ = 15

Thus;

z = (125 - 110)/15

z = 1

From the normal standard distribution table we can find the probability from the z-score as;

P(x > 95) = 1 - 0.158655.

P(x > 95) = 0.841

Read more about Probability from z-score at; https://brainly.com/question/25638875

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