1 
Solve the problem. 
A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If 40 different applicants are randomly selected, find the probability that their mean is above 215.  
0.0287 
0.1179 
0.3821 
0.4713 
2 
Select the correct response. 
Which biased estimator will have a reduced bias based on an increased sample size? 
median 
standard deviation 
range 
mean 
4 
Solve the problem. 
The scores on a certain test are normally distributed with a mean score of 43 and a standard deviation of 3. What is the probability that a sample of 90 students will have a mean score of at least 43.3162? 
0.8413 
0.1587 
0.3174 
0.3413 
5 
Solve the problem.  
Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. If 19 people are randomly selected, find the probability that their mean body temperature will be less than 98.50°F. 
0.0833 
0.9826 
0.4826 
0.3343 
6 
Provide an appropriate response. 
Samples of size n = 240 are randomly selected from the population of numbers (0 through 20) produced by a random-number generator, and the variance is found for each sample. What is the distribution of the sample variances? 
normal (approximately) 
skewed to the left 
skewed to the right 
not enough information provided 
7 
If z is a standard normal variable, find the probability.  
The probability that z is greater than “1.82 
0.4656 
0.0344 
“0.0344 
0.9656 
8 
Choose the correct response. 
Why are unbiased estimators preferred over biased estimators? 
Unbiased estimators retain the original distribution of the sample, where as biased estimators follow a normal distribution. 
Unbiased estimators follow the normal distribution, where as biased estimators follow the original distribution.  
Unbiased estimators behave with reliable results, where as biased estimators are inconsistent. 
Unbiased estimators require a greater sample size which gives greater accuracy over biased estimators. 
9 
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%. 
1078.3 
1148.1 
1087.8 
1021.7 
10 
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information.  
If 6.3% of the thermometers are rejected because they have readings that are too high and another 6.3% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others. 
“1.53° , 1.53° 
“1.45° , 1.45° 
“1.39° , 1.39° 
“1.46° , 1.46° 
11 
Provide an appropriate response.  
Find the indicated IQ score. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).  
The shaded area under the curve is 0.5675. 
110.7 
129.6 
97.5 
102.6 
*if you cant solve this cause there is no graph dont worry about it 
The answer is 102.6 if the area is on the left. 
The answer is 97.5 is the area is on the right. 
12 
Provide an appropriate response. 
Samples of size n = 15 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the standard deviation is found for each sample. What is the distribution of the sample standard deviations? 
not enough information provided 
skewed to the left 
skewed to the right 
normal (approximately) 
13 
Solve the problem. 
A math teacher gives two different tests to measure students’ aptitude for math. Scores on the first test are normally distributed with a mean of 23 and a standard deviation of 4.2. Scores on the second test are normally distributed with a mean of 71 and a standard deviation of 10.8. Assume that the two tests use different scales to measure the same aptitude. If a student scores 29 on the first test, what would be his equivalent score on the second test? (That is, find the score that would put him in the same percentile.) 
87 
77 
84 
86 
14 
Find the indicated probability. 
The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter of a randomly selected pencil will be less than 0.285 inches? 
0.0668 
0.9332 
0.4332 
0.0596 
15 
Solve the problem. 
Assume that women’s heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 90 women are randomly selected, find the probability that they have a mean height between 62.9 inches and 64.0 inches.  
0.9318 
0.1739 
0.7248 
0.0424 
16 
Provide an appropriate response. 
Samples of size n = 60 are randomly selected from the population of numbers (0 through 9) produced by a random-number generator, and the mean is taken for each sample. What is the dispnotribution of the sample means? 
pnonormal (approximately) 
not enough information provided 
skewed to the right 
skewed to the left 
17 
Solve the problem. 
In a recent study of animal sleep times at the zoo, the mean amount of sleep per night is 6.3 hours with a standard deviation of 2.1. If 23 animals are selected, find the probability that the mean sleep time per night is greater than 8 hours.  
0.2981 
0.3207 
0.0103 
0.0001 
18 
Using the following uniform density curve, answer the question.  
What is the probability that the random variable has a value greater than 2? 
0.7 
0.875 
0.625 
0.75 
*again I cant copy the graph on here so no problem if you can solve it 
The answer = (Max “ 2 ) / (Max “ Min). 
19 
If z is a standard normal variable, find the probability.  
The probability that z lies between “1.10 and “0.36 
0.2237 
0.2239 
“0.2237 
0.4951 
20 
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? 
0.4834 
0.0166 
0.0179 
0.9834