Question

A distribution has a mean of 90 and a standard deviation of 15. Samples of size 25 are drawn randomly from the population. Find the probability that the sample mean is more than 85 g

Answer 1

The probability is 0.04746

Explanation:

Firstly, we calculate the z-score here

Mathematically;

z-score = x-mean/SD/√n

Where from the question;

x = 85, mean = 90 , SD = 15 and n = 25

Plugging these values into the equation, we have;

Z = (85-90)/15/√25 = -5/15/5 = -1.67

So the probability we want to calculate is ;

P(z > -1.67)

We use the standard normal distribution table for this;

P(z > -1.67) = 0.04746