Question

Prices were recorded for all the loaves of bread in a supermarket, the mean price for a loaf of bread was $1.37 with a standard deviation of $0.67. Find the probability that if 13 loaves are selected the mean price is less than $1.00.

Answer 1

Answer: The real answer is 0.0233

Answer 2

The probability that if 13 loaves are selected the mean price is less than $1.00 is:
`P = 0.0287`

Explanation:

Let's say that μ is the average price of the loaves.

μ is the population mean. μ = $1.37

`\sigma` is the standard deviation and
`\sigma= \$0.67`

Then we take a sample of size n = 13

Where

`\mu_x` is the is the sample mean.

`\sigma_x` is the standard deviation of the sample

By definition:

`\sigma_x = (\sigma)/(√(n))`

`\sigma_x = (0.67)/(√(13)) = 0.1858`

We look for the probability that the mean of the sample is less than $ 1.00

This is:

`P(\mu_x< 1)`

Now we find the standard statistic standard Z.

`P(\mu_x< 1) = P((\mu_x-\mu)/(\sigma_x)<(1-1.37)/(0.1858))\\\\P(Z<(1-1.37)/(0.1858)) = P(Z<-1.99)`

By symmetry of the standard normal distribution:

`P(Z<-1.99) = P(Z>1.99)\\\\`

Looking in the standard normal table we get

`P(Z>1.99) = 0.0287`