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.


A 0.0032


B 0.5643


C 0.9105


D 0.0233

Answer 1

Answer:

$z = \frac{1-1.37}{\frac{0.67}{\sqrt{13}}} = -1.991$

And we want this probability:

$P(z<-1.991)$

And using the normal standard distribution or excel we got:

$P(z<-1.991)= 0.0233$

And the best option would be:

D 0.0233

Step-by-step explanation:

For this case we have the following parameters:

$\mu = 1.37, \sigma =0.67$

And we select a sample size of n=13. And we want to find this probability:

$P(\bar X <1)$

We can assume that the distribution for this case is normal and then we can use the z score formula given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we replace the data given we got:

$z = \frac{1-1.37}{\frac{0.67}{\sqrt{13}}} = -1.991$

And we want this probability:

$P(z<-1.991)$

And using the normal standard distribution or excel we got:

$P(z<-1.991)= 0.0233$

And the best option would be:

D 0.0233