Question

The CDC recommends that adults age 18 to 64 should exercise moderately for at least 150 minutes per week. The time that adults in California spend exercising per week is normally distributed with a mean of 153 minutes and a standard deviation of 10 minutes.

What is the probability that a random sample of size 30 Californians age 18 to 64 will have a mean exercise time within 3 minutes of the mean?
Illustrate by noting all relevant details on the normal curve below, and shading the appropriate region. You may use your calculator to determine the probability, and you must show the syntax of your calculator inputs.

Answer 1

This is a normal distribution question with

Sample size (n) = 30

Since we know that

P(150.0 < x < 156.0)=?

This implies that

P(150.0 < x < 156.0) = P(-1.6432 < z < 1.6432) = P(Z < 1.6432) - P(Z < -1.6432)

P(150.0 < x < 156.0) = 0.9498292200499503 - 0.05017077995004965

PS: you have to refer z score table to find the final probabilities.

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