**Statistics and Probability Homework Solution 3**

1. Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.

The current speed limit is 65 mph.

a. What proportion of vehicles travel less than or equal to the speed limit?

P(x<=65)=

Enter answer as a decimal rounded to 4 places with a 0 to the left of the decimal point.

Do not enter answer as a percent.

__________________

b. What proportion of the vehicles would be going less than or equal to 50 mph?

P(x<=50)=

Enter answer as a decimal rounded to 4 decimal places with a 0 to the left of the decimal point.

Do not enter answer as a percent.

___________________

c. A new speed limit (x) will be initiated such that 10% of vehicles will be equal to or over the speed limit.

What is the new speed limit (x) based on this criterion?

P(x>=X)=.10

Enter answer rounded to 1 decimal place.

___________________

2. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet.

If x = distance in feet for a fly ball, then x~_____(_____,_____) = x~___N__(_250_,_50_)

a. If a fly ball is randomly chosen from this distribution, what is the probability that the ball traveled fewer than 220 feet?

Enter answer rounded to 4 decimal places with 0 to the left of the decimal point. Do not enter answer as a percent.

___________________

b. Find the 80^{th} percentile of the distribution of fly balls. (At what distance or less will the ball travel 80% of the time.)

P(X<=X)=.80

Enter answer rounded to 0 decimal places.

(Enter answer as an integer.)

3. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet.

Answer the following questions pertaining to how far on average the balls will travel based based upon a randomly sample of 49 fly balls.

_

X is notation for the average value of the x’s.

1 What is the appropriate distribution for addressing the questions?

a Normal Population Distribution (parent)

b Normal Sampling Distribution

Select the appropriate distribution by entering the corresponding letter

2. What is the numerical value of the mean (mu) for the distribution?

Enter the numerical value of mu with 0 decimal place precision (Integer).

3. What is the standard deviation of the distribution of distances a fly ball travels on average, the standard error of the mean?

Enter answer with 2 decimal place precision.

____________________answer ____________________answer____________________answer

4. What is the probability that the 49 balls traveled an average distance of less than 240 feet?

_

The P(X < 240)=

Enter answer to 3 decimal place precicion.

Do not enter answer as a percent

Include a 0 to the left of the decimal point.

___________________

5. Find the 80^{th} percentile of the Sampling Distribution of Averages for the average of the 49 fly balls.

_ _

Find the X value such that P(X < X )=.80

___________________

4. A typical adult has an average IQ score of 105 with a standard deviation of 20.

If twenty (25) randomly selected adults are given an IQ test:

a. What is the probability that the sample mean (xbar) scores will be equal to or less than 100 points?

Find the probability that P(Xbar=<100)

Enter answer rounded to 2 decimal places

Include a 0 to the left of the decimal point if your answer is lessthan 1.

Do not enter answer as a percent.

________________

b. What is the probability that the sample mean scores will be between 100 and 115 points?

Find the probability that P(100<=x=<115)

Enter answer rounded to 3 decimal places with a 0 to the left of the decimal point.

Do not enter answer as a percent

_______________________

5. You take a sample of 22 from a population of test scores. The mean of your sample is 60 and the population standard deviation is 10.

1. What is the point estimate for the population mean?

Enter answer as an integer

_______________________

2. What is the 95% confidence interval for the population mean?

Enter the lower number of the conference interval for the first number and the upper number of the conference interval for the second number.

Enter each number rounded to 1 decimal place

____________________ _________________________

3. What is the 99% confidence interval for the population mean?

Enter the lower number of the conference interval for the first number and the upper number of the conference interval for the second number.

Enter each number rounded to 1 decimal place.

____________________ _________________________

4. What parameter would you have to change to change the confidence level?

a. The z value

b. The size of the sample size n.

c Neither the z value of the sample size n. You would have to change the point estimate.

Would the above change effect the width of the confidence interval?

a. Yes, the above change would effect the width of the confidence interval?

b. No, the above change would not effect the width of the confidence interval?

Answer the above questions by entering the appropriate letter in the order in which the questions were asked.

_______________________ ________________________

5. What parameter would you have to change to change the width of the confidence interval that would not change the confidence level?

a. The z value

b. The size of the sample size n.

c. Neither the z value or the sample size n. You would have to change the point estimate.

Enter the appropriate letter for answering this question.

___________________________

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