Question 1

In a certain state, the daily amounts of industrial waste are normally distributed, with a mean of 5,000 tons and a standard deviation of 1,500 tons. Find the probability that on a randomly selected day the amount of industrial waste is greater than 6,695 tons. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​

Accepted Answer

A)  ​0.1292 
B)  ​0.8708 
C)  ​0.5050 
D)  ​0.3609 
E)  ​0.3876

Question 2

Determine c, if possible, so that the formula  describes a discrete probability distribution. ​

Accepted Answer

A)  11 
B)   
C)  35 
D)  ​  
E)  not possible

Question 3

Find the variance of the set of sample data. ​
83, 89, 87, 99, 92, 99
​

Accepted Answer

A)  42.3 
B)  90.5 
C)  91.5 
D)  549 
E)  6.5

Question 4

In a binomial experiment find the probability of no more than 89 successes in 114 trials if  . Round your answer to four decimal places. ​

Accepted Answer

A)  0.6305 
B)  0.0239 
C)  0.4761 
D)  0.7337 
E)  0.9761

Question 5

Suppose that the duration of the mating calls of a population of tree toads are normally distributed, with mean 188 milliseconds (msec) and standard deviation 40 msec. What proportion of these calls would be expected to last between 192 and 268 msec? Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​

Accepted Answer

A)  0.5626 
B)  0.9374 
C)  0.4374 
D)  0.1874 
E)  0.1750

Question 6

The table below gives the votes in favor of the measure "Amend the state constitution to recognize marriage only between a man and a woman" in states that had it on the ballot. What is the mean of the state percents favoring this measure? Round your answer to two decimal places. ​

Accepted Answer

A)  70.00 
B)  73.36 
C)  67.25 
D)  16.14 
E)  80.70

Question 7

A variable x has a binomial distribution with probability of success 0.65 for each trial. For a total of 50 trials, what are the mean and the standard deviation of the distribution? ​

Accepted Answer

A)   ​ 
B)   ​ 
C)   ​ 
D)   ​ 
E)   ​

Question 8

Find the median of the set of scores. ​
24)8, 28.4, 27.3, 27.3, 29.2
​

Accepted Answer

A)  28.4 
B)  29.2 
C)  12.4 
D)  13.7 
E)  27.3

Question 9

A nonprofit organization sells chances for a $40,000 automobile at $125 per ticket. It sells 2,000 tickets and offers four prizes, summarized in the table that follows. What are the expected winnings (or loss) for each ticket? ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

In a certain state, the daily amounts of industrial waste are normally distributed, with a mean of 6,000 tons and a standard deviation of 2,000 ons. Find the probability that on a randomly selected day the amount of industrial waste is between 9,400 and 11,800 tons. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​

Accepted Answer

A)  0.0427 
B)  0.9573 
C)  0.2911 
D)  0.4270 
E)  0.4697

Question 11

Suppose the probability of suicide among a certain age group is 0.006. If a randomly selected group of 150 Native Americans within this age group had no suicides, find the probability of this occurring by chance. Round your answer to four decimal places. ​

Accepted Answer

A)  0.3818 
B)  0.3595 
C)  0.4055 
D)  0.2221 
E)  0.2661

Question 12

An insurance company insures 100,000 cars in a certain area. The company has determined that on average, each year they will have to pay the following amounts for accidents in the area: ​
$100,000 with probability 0.0004
$50,000 with probability 0.001
$25,000 with probability 0.006
$5000 with probability 0.011
$1000 with probability 0.023
​
What is the company's expected payout per car each year?
​

Accepted Answer

A)  $318.00 
B)  $4163.00 
C)  $4140.00 
D)  $381.60 
E)  $279.84

Question 13

In studying a certain endangered species, scientists have found that when the animals are relocated, it takes x years without offspring before the first young are born, where x and the probability of x are given below. What is the expected number of years before the first young are born? ​

Accepted Answer

A)  1.96 years 
B)  0.96 years 
C)  0.64 years 
D)  1.56 years 
E)  1.68 years

Question 14

Which frequency table best describes the data displayed in the frequency histogram? ​  ​

Accepted Answer

A)  
B)  
C)  
D)  
E)

Question 15

Suppose a pair of dice is thrown 11 times. What is the probability that a sum of 10 occurs exactly 4 times? Round your answer to six decimal places. ​

Accepted Answer

A)  0.022053 
B)  0.043112 
C)  0.071062 
D)  0.008655 
E)  0.103840

Question 16

Use a table of the standard normal distribution to find the probability that a z-score from the standard normal distribution will lie within the interval  . Round your answer to four decimal places. ​

Accepted Answer

A)  0.4643 
B)  0.9285 
C)  0.0715 
D)  0.1715 
E)  0.6964

Question 17

In a certain state, the daily amounts of industrial waste are normally distributed, with a mean of 9,000 tons and a standard deviation of 1,000 tons. Find the probability that on a randomly selected day the amount of industrial waste is less than 7,000 tons. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​

Accepted Answer

A)  0.9772 
B)  0.1836 
C)  0.7936 
D)  0.0228 
E)  0.7720

Question 18

Suppose a standardized exam for admission to a special program has been passed by 54% of the students taking it over the last five years. Suppose that 1368 of 2400 students taking the test this year pass. What is the probability that at least 1368 would pass if the pass rate is 54%? Round your answer to four decimal places. ​

Accepted Answer

A)  0.0017 
B)  0.9983 
C)  0.1072 
D)  0.2956 
E)  0.4000

Question 19

If a fair coin is tossed 123 times, what is the probability that no more than 67 heads will occur? Round your answer to four decimal places. ​

Accepted Answer

A)  0.5141 
B)  0.6483 
C)  0.1401 
D)  0.7738 
E)  0.8599

Question 20

Suppose that the ratio of boys born to girls born is 120 to 100, what is the probability that out of 2500 babies born in Santa Clara, 1180 will be girls? Round your answer to four decimal places. ​

Accepted Answer

A)  0.9966 
B)  0.2044 
C)  0.4721 
D)  0.0034 
E)  0.2460

Exam 8: Further Topics in Probability and Data Description

Determine c, if possible, so that the formula describes a discrete probability distribution.

Find the variance of the set of sample data. 83, 89, 87, 99, 92, 99

In a binomial experiment find the probability of no more than 89 successes in 114 trials if . Round your answer to four decimal places.

The table below gives the votes in favor of the measure "Amend the state constitution to recognize marriage only between a man and a woman" in states that had it on the ballot. What is the mean of the state percents favoring this measure? Round your answer to two decimal places.

A variable x has a binomial distribution with probability of success 0.65 for each trial. For a total of 50 trials, what are the mean and the standard deviation of the distribution?

Find the median of the set of scores. 24) 8, 28.4, 27.3, 27.3, 29.2

A nonprofit organization sells chances for a $40,000 automobile at $125 per ticket. It sells 2,000 tickets and offers four prizes, summarized in the table that follows. What are the expected winnings (or loss) for each ticket?

Suppose the probability of suicide among a certain age group is 0.006. If a randomly selected group of 150 Native Americans within this age group had no suicides, find the probability of this occurring by chance. Round your answer to four decimal places.

In studying a certain endangered species, scientists have found that when the animals are relocated, it takes x years without offspring before the first young are born, where x and the probability of x are given below. What is the expected number of years before the first young are born?

Which frequency table best describes the data displayed in the frequency histogram?

Suppose a pair of dice is thrown 11 times. What is the probability that a sum of 10 occurs exactly 4 times? Round your answer to six decimal places.

Use a table of the standard normal distribution to find the probability that a z-score from the standard normal distribution will lie within the interval . Round your answer to four decimal places.

If a fair coin is tossed 123 times, what is the probability that no more than 67 heads will occur? Round your answer to four decimal places.

Suppose that the ratio of boys born to girls born is 120 to 100, what is the probability that out of 2500 babies born in Santa Clara, 1180 will be girls? Round your answer to four decimal places.