Question

A can of Pepsi is supposed to contain, on the average, 12 ounces of soda with a standard deviation of 0.3 ounces. Suspecting fraud, you take a random sample of 40 cans and measure the amount of Pepsi in each. Your measurements show that the 40 cans had a mean of11.9 ounces. What is the probability of a random sample of 40 cans having a mean of 11.9 ounces of soda or less

Answer 1

The probability of a random sample of 40 cans having a mean of 11.9 ounces of soda or less is 1.8%

Z score

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

$z=\frac{x-\mu}{\sigma/\sqrt{n} }$

Where x is raw score, μ is mean, σ is standard deviation and n is sample size.

Given that:

σ = 0.3, n = 40, μ = 12, hence for x <  11.9:

$z=\frac{11.9-12}{0.3/\sqrt{40} } =-2.1$

From the normal table, P(z < -2.1) = 1.8%

The probability of a random sample of 40 cans having a mean of 11.9 ounces of soda or less is 1.8%

Find out more on Z score at: brainly.com/question/25638875