Answer:
The probability that if 13 loaves are selected the mean price is less than $1.00 is: [tex]P = 0.0287[/tex]
Step-by-step explanation:
Let's say that μ is the average price of the loaves.
μ is the population mean. μ = $1.37
[tex]\sigma[/tex] is the standard deviation and [tex]\sigma= \$0.67[/tex]
Then we take a sample of size n = 13
Where
[tex]\mu_x[/tex] is the is the sample mean.
[tex]\sigma_x[/tex] is the standard deviation of the sample
By definition:
[tex]\sigma_x = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]\sigma_x = \frac{0.67}{\sqrt{13}} = 0.1858[/tex]
We look for the probability that the mean of the sample is less than $ 1.00
This is:
[tex]P(\mu_x< 1)[/tex]
Now we find the standard statistic standard Z.
[tex]P(\mu_x< 1) = P(\frac{\mu_x-\mu}{\sigma_x}<\frac{1-1.37}{0.1858})\\\\P(Z<\frac{1-1.37}{0.1858}) = P(Z<-1.99)[/tex]
By symmetry of the standard normal distribution:
[tex]P(Z<-1.99) = P(Z>1.99)\\\\[/tex]
Looking in the standard normal table we get
[tex]P(Z>1.99) = 0.0287[/tex]
