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1) Using the following uniform density curve, answer the question.
What is the probability that the random variable has a value between 0.2 and 0.8?
Answer:
A) 0.075
B) 0.325
C) 0.05
D) 0.2
2) Using the following uniform density curve, answer the question.
What is the probability that the random variable has a value less than 3.4?
Answer:
A) 0.1750
B) 0.3000
C) 0.4250
D) 0.5500
3) Using the following uniform density curve, answer the question.
What is the probability that the random variable has a value greater than 5.5?
Answer:
A) 0.4375
B) 0.2625
C) 0.3125
D) 0.1875
4) Using the following uniform density curve, answer the question.
What is the probability that the random variable has a value less than 7?
Answer:
A) 1.000
B) 0.750
C) 0.625
D) 0.875
5) Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
Shaded area is 0.4483.
Answer:
A) 0.3264
B) 0.13
C) 0.6736
D) -0.13
6) Using the following uniform density curve, answer the question.
What is the probability that the random variable has a value less than 2.5?
Answer:
A) 0.1875
B) 0.4375
C) 0.0625
D) 0.3125
7) Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost.
Between 7 pounds and 10 pound
8) Assume that X has a normal distribution, and find the indicated probability.
The mean is = 15.2 and the standard deviation is = 0.9.
Find the probability that X is greater than 16.1.
Answer:
A) 0.1357
B) 0.1550
C) 0.1587
D) 0.8413
9) Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost.
Between 8.5 pounds and 10 pounds
10) Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
Answer:
A) 0.0301
B) 0.0602
C) 0.9699
D) 0.9398
11) Find the indicated probability.
The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days?
Answer:
A) 0.0179
B) 0.0166
C) 0.9834
D) 0.4834
12) Assume that X has a normal distribution, and find the indicated probability.
The mean is = 15.2 and the standard deviation is = 0.9.
Find the probability that X is greater than 17.
Answer:
A) 0.9713
B) 0.9772
C) 0.0228
D) 0.9821
13) Solve the problem.
In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of and a standard deviation of If 50 different homes are randomly selected, find the probability that their mean energy consumption level for September is greater than
Answer:
A) 0.2090
B) 0.2910
C) 0.0438
D) 0.4562
14) Assume that X has a normal distribution, and find the indicated probability.
The mean is = 60.0 and the standard deviation is = 4.0.
Find the probability that X is less than 53.0.
Answer:
A) 0.5589
B) 0.0401
C) 0.9599
D) 0.0802
15) Solve the problem.
If a continuous uniform distribution has parameters of and then the minimum is and the maximum is For this distribution, find Round your answer to three decimal places.
Answer:
A) 0.577
B) 0.722
C) 0.417
D) 0.866
16) Find the indicated value.
z0.10
Answer:
A) 1.58
B) 1.17
C) 1.05
D) 1.28
17) Solve the problem. Round to the nearest tenth unless indicated otherwise.
Scores on an English test are normally distributed with a mean of 37.6 and a standard deviation of 7.6. Find the score that separates the top 59% from the bottom 41%
Answer:
A) 39.3
B) 42.1
C) 33.1
D) 35.9
18) Solve the problem.
In a game of roulette, Jorge places 170 bets of each on the number 3. A win pays off with odds 35:1 and on any one spin there is a probability that 3 will be the winning number. Among the 170 bets, what is the minimum number of wins needed for Jorge to make a profit? Estimate the probability that Jorge will make a profit.
Answer:
A) 6; 0.2327
B) 5: 0.4013
C) 5; 0.496
D) 6; 0.3121
19) Solve the problem. Round to the nearest tenth unless indicated otherwise.
In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. Find P45, which is the consumption level separating the bottom 45% from the top 55%.
Answer:
A) 1078.3
B) 1021.7
C) 1087.8
D) 1148.1
20) Solve the problem. Round to the nearest tenth unless indicated otherwise.
Suppose that replacement times for washing machines are normally distributed with a mean of 10.8 years and a standard deviation of 1.4 years. Find the replacement time that separates the top 18% from the bottom 82%.
Answer:
A) 9.5 years
B) 11.1 years
C) 11.3 years
D) 12.1 years
21) Provide an appropriate response.
The number of books sold over the course of the four-day book fair were 178, 148, 216, and 64. Assume that samples of size 2 are randomly selected with replacement from this population of four values. Identify the probability of each sample, and describe the sampling distribution of the sample means.
Answer:
22) Provide an appropriate response.
The number of books sold over the course of the four-day book fair were 140, 163, 206, and 90. Assume that samples of size 2 are randomly selected with replacement from this population of four values. Identify the probability of each sample, and describe the sampling distribution of the sample means.
Answer:
23) Provide an appropriate response.
Personal phone calls received in the last three days by a new employee were 2, 4, and 7. Assume that samples of size 2 are randomly selected with replacement from this population of three values. Identify the probability of each sample, and describe the sampling distribution of the sample means.
Answer:
24) Provide an appropriate response.
Consider the uniform distribution shown below. Find the probability that x is greater than 6. Discuss the relationship between area under a density curve and probability.
