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P(A1) = .20, P(A2) = .40, and P(A3) = .40. P(B1|A1) = .25. P(B1|A2) = .05, and P(B1|A3) = .10.

QUESTION 1






P(A1) = .20, P(A2) = .40, and P(A3) = .40.  P(B1|A1) = .25. P(B1|A2) = .05, and P(B1|A3) = .10.

 






Use Bayes’ theorem to determine P(A3|B1). (Round your answer to 4 decimal places.)

 







  P(A3|B1)

 

QUESTION 2






The U.S. Postal Service reports 95% of first-class mail within the same city is delivered within 2 days of the time of mailing. Six letters are randomly sent to different locations.

 











a.What is the probability that all six arrive within 2 days? (Round your answer to 4 decimal places.)

 







  Probability

 











b.What is the probability that exactly five arrive within 2 days? (Round your answer to 4 decimal places.)

 







  Probability

 











c.Find the mean number of letters that will arrive within 2 days. (Round your answer to 1 decimal place.)

 







  Number of letters

 











d-1.Compute the variance of the number that will arrive within 2 days. (Round your answer to 3 decimal places.)

 







  Variance

 











d-2.Compute the standard deviation of the number that will arrive within 2 days. (Round your answer to 4 decimal places.)

 







  Standard Deviation

 






QUESTION 3In a binomial distribution, n = 12 and π = .60.

 







a.Find the probability for x = 5? (Round your answer to 3 decimal places.)

 







  Probability

 







b.Find the probability for x ≤ 5? (Round your answer to 3 decimal places.)

 







  Probability

 







c.Find the probability for x ≥ 6? (Round your answer to 3 decimal places.)

 







  Probability

 






A population consists of 15 items, 10 of which are acceptable.

 






QUESTION 4In a sample of four items, what is the probability that exactly three are acceptable? Assume the samples are drawn without replacement. (Round your answer to 4 decimal places.)

 







  Probability

 






QUESTION 5

According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts.

 











a.What is the mean amount spent on insurance?

 







  Mean$

 











b.What is the standard deviation of the amount spent? (Round your answer to 2 decimal places.)

 







  Standard deviation$

 











c.If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year? (Round your answer to 4 decimal places.)

 


















  Probability
QUESTION 6

The mean of a normal probability distribution is 60; the standard deviation is 5. (Round your answers to 2 decimal places.)

 











a.About what percent of the observations lie between 55 and 65?

 







  Percentage of observations%

 











b.About what percent of the observations lie between 50 and 70?

 







  Percentage of observations%

 











c.About what percent of the observations lie between 45 and 75?

 

















  Percentage of observations%
QUESTION 7

 

A normal population has a mean of 12.2 and a standard deviation of 2.5.

 











a. Compute the z value associated with 14.3. (Round your answer to 2 decimal places.)

 







  Z

 











b. What proportion of the population is between 12.2 and 14.3? (Round your answer to 4 decimal places.)

 







  Proportion

 











c. What proportion of the population is less than 10.0? (Round your answer to 4 decimal places.)

 


















  Proportion
 

QUESTION 8

 

A normal population has a mean of 80.0 and a standard deviation of 14.0.

 











a.Compute the probability of a value between 75.0 and 90.0. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)

 







  Probability

 











b.Compute the probability of a value of 75.0 or less. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)

 







  Probability

 











c.Compute the probability of a value between 55.0 and 70.0. (Round intermediate calculations to 2 decimal places. Round final answer to 4 decimal places.)

 










  Probability
QUESTION 9

 

For the most recent year available, the mean annual cost to attend a private university in the United States was $26,889. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,500.

 









Ninety-five percent of all students at private universities pay less than what amount? (Round z value to 2 decimal places and your final answer to the nearest whole number.)

 







  Amount$

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