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AP® Statistics

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Moderate

Probability Greater Calorie Savings

APSTAT-TU1NKN

A national Italian restaurant has created a healthy option to one of its most popular dishes.

The original dish’s portion size has a mean $\mu$ of $1,500$ calories with a standard deviation of $50$ calories, and the healthy alternative’s portion size has a mean $\mu$ of $950$ calories with standard deviation of $25$ calories.

The resulting distribution of the calorie savings by choosing the healthy option over the original dish has a mean $\mu$ of $550$ calories saved and standard deviation $\sigma$ of $55.9$ calories. John and Mary go to the restaurant, and both order the healthy option.

What is the probability that their average calorie savings is equal to or greater than $600$ calories when John and Mary both opt for the healthier alternative?

A

$0.04$

B

$0.1$

C

$0.19$

D

$0.81$

E

$0.9$