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# Question 7 (1 point) The rainfall in Aberdeen Reservoir, Washington (the wettest place in the contiguous...

Question 7 (1 point)

The rainfall in Aberdeen Reservoir, Washington (the wettest place in the contiguous United States) averages 137.36 inches per year with a standard deviation of 6.27 inches. According to the Central Limit Theorem, what happens to the histogram of averages as n increases?

Question 7 options:

 1) The histogram will begin to look more like the normal curve.
 2) The histogram will begin to look less like the normal curve.
 3) Increasing n will not affect the histogram of averages.
 4) It depends on the mean and standard deviation.
 5) The histogram will begin to look more like the original distribution.

Question 8 (1 point)

Historically, the average score of PGA golfers for one round is 71.1 with a standard deviation of 3.05. A random sample of 73 golfers is taken. What is the probability that the sample mean is greater than 71?

Question 8 options:

 1) 0.3897
 2) 0.4869
 3) -0.0746
 4) 0.6103
 5) 0.5131

Question 9 (1 point)

Energetic Co., a battery manufacturer, claims their battery lasts for 66.04 months with a standard deviation of 14.205 months. You randomly sample 25 of these batteries. Assuming the distribution for the battery lifetime is approximately normal, what is the probability the average lifetime is less than 68.01?

Question 9 options:

 1) 0.244
 2) 0.1104
 3) 0.5551
 4) 0.4449
 5) 0.756

Question 10 (1 point)

Fill in the blank. Suppose that the average starting salary for student with an Economics degree is \$51,043.48 with a standard deviation of \$9,925.81. A random sample of 159 recent graduates with a job is taken. There is a 23% chance that the average salary is greater than \$ ________.

Question 10 options:

 1) 43,709.83
 2) 51,625.08
 3) There is not enough information to determine this.
 4) 58,377.13
 5) 50,461.88

Question 11 (1 point)

Fill in the blank. In a drive thru performance study, the average service time for McDonald's is 203.21 seconds with a standard deviation of 5.67 seconds. A random sample of 90 times is taken. There is a 51% chance that the average drive-thru service time is less than ________ seconds.

Question 11 options:

 1) There is not enough information to determine this.
 2) 203.07
 3) 203.22
 4) 203.2
 5) 203.35

7)]

 The histogram will begin to look more like the normal curve.

8)

 std error=σx̅=σ/√n= 0.35698
 probability =P(X>71)=P(Z>(71-71.1)/0.357)=P(Z>-0.28)=1-P(Z<-0.28)=1-0.3897=0.6103

9)

 std error=σx̅=σ/√n= 2.841
 probability =P(X<68.01)=(Z<68.01-66.04)/2.841)=P(Z<(0.69)=0.756

10)since top 23 % values are (100-23=77th percentile):

 for 77th percentile critical value of z= 0.74 therefore corresponding value=mean+z*std deviation= 51625.08

11)

 for 51th percentile critical value of z= 0.03 therefore corresponding value=mean+z*std deviation= 203.2

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