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 95% chance that the grocery store sells more than 390 tomatoes in a week.
b. there is an 84% chance that the grocery store sells more than 390 tomatoes in a week.
c. there is a 68% chance that the grocery store sells fewer than 390 tomatoes in a week.
d. there is a 34% chance that the grocery store sells fewer than 390 tomatoes in a week.

Explanation:

Step1: Identify z - score

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

Step2: Use normal distribution properties

In a normal distribution, the area to the left of $z=-1$ is approximately $0.16$ (or 16%). So the area to the right of $z = - 1$ (probability of selling more than 390 tomatoes) is $1 - 0.16=0.84$ (or 84%).

Let's analyze other options:

• Option A: The area to the right of $z=-1$ is 84%, not 95%. 95% of the data is within $z=- 2$ and $z = 2$.
• Option C: 68% of the data is within $z=-1$ and $z = 1$. The probability of selling fewer than 390 (z=-1) is 16%, not 68%.
• Option D: The probability of selling fewer than 390 (z=-1) is 16%, not 34%.

Answer:

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