The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience.
 

 

Admissions Probability
1,050 0.3
1,280 0.1
1,560 0.6
 

 

1. What is the expected number of admissions for the fall semester? 5309
   

 

  Expected number of admissions: 1379  

 

2. Compute the variance and the standard deviation of the number of admissions. (Round your standard deviation to 2 decimal places.)
   

 

   
  Variance :53109  
 Standard deviation: 230.45  

 

2.

 

It is asserted that 70% of the cars approaching an individual toll booth in New Jersey are equipped with an E-ZPass transponder. Find the probability that in a sample of five cars:

 

a. All five will have the transponder. (Round your answer to 4 decimal places.)
   

 

  Probability: 0.1681  

 

b. At least three will have the transponder. (Round your answer to 4 decimal places.)
   

 

  Probability: 0.8369  

 

c. None will have a transponder. (Round your answer to 6 decimal places.) 0.002430
   

 

  Probability: 0.00243  

 

3.

 

The Internal Revenue Service is studying the category of charitable contributions. A sample of 24 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 24 returns, 8 had charitable contributions of more than $1,000. Suppose 7 of these returns are selected for a comprehensive audit.
 a You should use the hypergeometric distribution is appropriate. Because
   
  hypergeometric distribution is appropriate because the selection is without replacements

 

 

 

b. What is the probability exactly one of the seven audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.)
     Probability 0.1851  

 

c. What is the probability at least one of the audited returns had a charitable contribution of more than $1,000? (Round your answer to 4 decimal places.)

 

  Probability: 0.9669  

 

Recent crime reports indicate that 4.8 motor vehicle thefts occur each minute in the United States. Assume that the distribution of thefts per minute can be approximated by the Poisson probability distribution.

 

a. Calculate the probability exactly three thefts occur in a minute. (Round your answer to 3 decimal places.)

 

  Probability: 0.152  

 

b. What is the probability there are no thefts in a minute? (Round your answer to 3 decimal places.)

 

  Probability: 0.008  

 

c. What is the probability there is two or less thefts in a minute? (Round your answer to 3 decimal places.)

 

  Probability: 0.143  

 

 

The mean of a normal probability distribution is 320; the standard deviation is 18.

 

a. About 68% of the observations lie between what two values?

 

   
  Value 1: 302  
  Value 2: 388  

 

b. About 95% of the observations lie between what two values?

 

   
  Value 1: 284  
  Value 2: 356  

 

c. Practically all of the observations lie between what two values?

 

   
  Value 1: 266  
  Value 2: 375  
6.

A normal population has a mean of 19 and a standard deviation of 5.

 

a. Compute the z value associated with 22. (Round your answer to 2 decimal places.)

 

  Z: 0.60  

 

b. What proportion of the population is between 19 and 22? (Round  z-score computation to 2 decimal places and your final answer to 4 decimal places.)

 

  Proportion: 0.2257  

 

c. What proportion of the population is less than 14? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

 

  Proportion: 0.1587  

7.

The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 29 million with a standard deviation of 4 million.

 

What is the probability next week’s show will:

 

a. Have between 31 and 38 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

 

  Probability: 0.2963  

 

b. Have at least 20 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

 

  Probability: 0.9878  

 

c. Exceed 35 million viewers? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

 

  Probability: 0.668  

8.

Waiting times to receive food after placing an order at the local Subway sandwich shop follow an exponential distribution with a mean of 46 seconds. Calculate the probability a customer waits:

 

a. Less than 26 seconds. (Round your answer to 4 decimal places.)

 

  Probability: 0.4318  

 

 

 

b. More than 105 seconds. (Round your answer to 4 decimal places.)

 

  Probability: 0.1020  

 

 

c. Between 38 and 60 seconds. (Round your answer to 4 decimal places.)

 

  Probability: 0.1664  

 

 

 

d. Fifty percent of the patrons wait less than how many seconds? What is the median? (Round your answer to 2 decimal places.)

 

  Median: 31.88   seconds