Question

select the correct answer. the number of tomatoes sold weekly by a grocery store follows a normal distribution with a mean of 455 and a standard deviation of 65. which sentence summarizes this information? a. there is a 68% chance that the grocery store sells fewer than 390 tomatoes in a week. b. there is a 95% chance that the grocery store sells more than 390 tomatoes in a week. c. there is an 84% chance that the grocery store sells more than 390 tomatoes in a week. d. there is a 94% chance that the grocery store sells fewer than 390 tomatoes in a week.

Explanation:

Step1: Calculate z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 390$, $\mu=455$, and $\sigma = 65$. So $z=\frac{390 - 455}{65}=\frac{- 65}{65}=-1$.

Step2: Use z - table

Looking up the z - score of - 1 in the standard normal distribution table, the cumulative probability $P(Z < - 1)=0.1587\approx16\%$. The probability of selling more than 390 is $P(Z>-1)=1 - P(Z < - 1)=1 - 0.1587 = 0.8413\approx84\%$.

Answer:

C. There is an 84% chance that the grocery store sells more than 390 tomatoes in a week.