select the correct answer.\nthe number of tomatoes sold weekly by a grocery store follows a normal…

select the correct answer.\nthe 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?\na. there is a 95% chance that the grocery store sells more than 390 tomatoes in a week.\nb. there is a 34% chance that the grocery store sells fewer than 390 tomatoes in a week.\nc. there is a 68% chance that the grocery store sells fewer than 390 tomatoes in a week.\nd. there is an 84% chance that the grocery store sells more than 390 tomatoes in a week.

select the correct answer.\nthe 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?\na. there is a 95% chance that the grocery store sells more than 390 tomatoes in a week.\nb. there is a 34% chance that the grocery store sells fewer than 390 tomatoes in a week.\nc. there is a 68% chance that the grocery store sells fewer than 390 tomatoes in a week.\nd. there is an 84% chance that the grocery store sells more than 390 tomatoes in a week.

Answer

Explanation:

Step 1: Calculate the z - score

The formula for the z - score is (z=\frac{x - \mu}{\sigma}), where (x = 390), (\mu=455), and (\sigma = 65). [ \begin{align*} z&=\frac{390 - 455}{65}\ &=\frac{- 65}{65}\ &=-1 \end{align*} ]

Step 2: Use the properties of the standard normal distribution

The total area under the normal curve is (1). The area to the left of (z = - 1) is (0.16) (from the standard normal table), and the area to the right of (z=-1) is (P(X>390)=1 - P(X < 390)). Since (P(X < 390)=0.16), then (P(X>390)=1-0.16 = 0.84) or (84%)

Answer:

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