introduction to statistics

Question 1

0 / 25 points

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.

________

Question 2

0 / 25 points

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.

  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 80th 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.)

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Question 3

0 / 25 points

A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4.

a.    Everyone who scores in the top 30% of the distribution gets a certificate. What is the        lowest  score (X) someone can get and still earn a certificate?

P(x>= X)  =  .30

Enter answer rounded to 1 decimal place.

________

 

 b.   The top 5% of the scores get to compete in a statewide history contest.

What is the lowest score (X) someone can get and still go onto compete with the rest of the state?

P(x>= X) = .05

Enter answer rounded to 1 decimal place.

________

Question 4

0 / 25 points

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 between 85 and 125 points?

Find the probability that P(85 <= Xbar =< 125)

Enter answer to 0 or 1 decimal place which ever is appropriate. Include a 0 to the left of the decimal point if your answer is less than 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 to 3 decimal places with a 0 to the left of the decimal point.

Do not enter answer as a percent.

________