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Ana is a dedicated Skee Ball player who always rolls for the 50-point slot.

Ana鈥檚 score Xon a randomly selected roll of the ball has the probability distribution

shown here with mean X=23.8and standard deviation X=12.63.

A player receives one ticket from the game for every 10points scored. Define T=number of tickets Ana gets on a randomly selected roll.

a. What shape does the probability distribution of Thave?

b. Find the mean of T.

c. Calculate the standard deviation ofT.

Short Answer

Expert verified

a. The distribution is skewed to the right, and Thas the same shape as the distribution.

b. The average number of tickets received on a randomly selected roll is 2.38.

c. Any given roll varies on average by 1.236from the mean number of tickets.

Step by step solution

01

Part(a) Step 1 : Given Information  

Probability distribution :

Mean : X=23.8

Standard deviation :X=12.63.

02

Part(a) Step 2 : Simplification  

For every 10points score one ticket is received it means that

Total number of tickets(T)=Numberofpoints10

If each data point is divided by the constant, the form of the distribution stays unchanged. Because the lowest bar in the histogram is to the right and the head of higher bars is to the right, the distribution is skewed to the right, and Thas the same shape as the distribution.

03

Part(b) Step 1 : Given Information  

Probability distribution :

Mean :X=23.8

Standard deviation :X=12.63.

04

Part(b) Step 2 : Simplification  

M=M10=23.810=2.38

One ticket is given for every ten points earned, implying that

The total number of tickets(T)=Numberofpoints10

As a result, if all of the data is split by the constant, the distribution's center will be changed in the same way, and the mean will be divided by the same constant 10.

05

Part(c) Step 1 : Given Information  

Probability distribution :

Mean :X=23.8

Standard deviation : X=12.63.

06

Part(c) Step 2 : Simplification  

m=X10=12.6310=1.263

One ticket is given for every ten points earned, implying that

The total number of tickets (T)=Numberofpoints10

So, if every piece of data is divided by the constant, the spread of the distributionTwill be affected in the same way, so the standard deviation is also dived by the same constant 10, and the number of tickets received on any given roll varies on average by 1.236from the mean number of tickets.

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