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Chapter 6: Q. 38 (page 384)

Total gross profits G on a randomly selected day at Tim’s Toys follow a distribution that is approximately Normal with mean \(560 and standard deviation \)185. The cost of renting and maintaining the shop is $65 per day. Let P=profit on a randomly selected day, so P=G−65. Describe the shape, center, and variability of the probability distribution of P.

Short Answer

Expert verified

P is a normal distribution with a mean of $495 and a standard deviation of $185.

Step by step solution

01

Given information

Given :

Total gross profits on a randomly selected day : G

It is approximately Normal with mean :$560

Standard deviation : $185.

The cost of renting and maintaining the shop is :$65

LetP=profit on a randomly selected day

⇒P=G−65.

02

Describing the shape, center, and variability of the probability distribution of P.

Shape :

Pis a normal distribution function because subtracting the constant from each data value has no effect on the shape of the distribution.

Center :

Pis a normal distribution function because when the constant is subtracted from each data value, the center of the distribution is also decreased by that constant value.

μp=μG–65=560–65=495

Spread :

Subtracting the constant from each data value has no effect on the distribution's spread; it remains unaffected.

σp=σg=185

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