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1 Six different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings (in mmHg) are listed below. Find the range, variance, and standard deviation for the given sample data. If the subject’s blood pressure remains constant and the medical students correctly apply the same measurement technique, what should be the value of the standard deviation?
145 124 130 146 136
Range = ________________________mmHg
Sample variance = ___________________mmHg(squared2) (Round to the nearest tenth as needed.)
Sample standard deviation = _____________________________ mmHg (Round to the nearest tenth as needed.)
What should be the value of the standard deviation?
A.Ideally, the standard deviation would be one because all the measurements should be the same.
B.Ideally, the standard deviation would be one because this is the lowest standard deviation that can be achieved.
C.Ideally, the standard deviation would be zero because all the measurements should be the same.
D.There is no way to tell what the standard deviation should be.
2 Heights of men on a baseball team have a bell-shaped distribution with a mean of 183 cm183 cm and a standard deviation of 6 cm6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?
a. 165 cm and 201 cm
b. 171 cm and 195 cm
a. __________% of the men are between 165165 cm and 201201 cm.(Do not round.)
b. ____________% of the men are between 171171 cm and 195195 cm.(Do not round.)
3. Heights of women have a bell-shaped distribution with a mean of 165165 cm and a standard deviation of 66 cm. Using Chebyshev’s theorem, what do we know about the percentage of women with heights that are within 22 standard deviations of the mean? What are the minimum and maximum heights that are within 22 standard deviations of the mean?
At least ____________% of women have heights within 22 standard deviations of 165165 cm.
(Round to the nearest percent as needed.)
The minimum height that is within 22 standard deviations of the mean is ___________ cm.
The maximum height that is within 22 standard deviations of the mean is _____________cm.
4 The table below lists probabilities for the corresponding numbers of girls in three births. What is the random variable, what are its possible values, and are its values numerical?
Number of girls x P(x)
0 0.125
1 0.375
2 0.375
3 0.125
Choose the correct answer below.
A.The random variable is P(x), which is the probability of a number of girls in three births. The possible values of P(x) are 0.125 and 0.375. The values of the random value P(x) are not numerical.
B.The random variable is x, which is the number of girls in three births. The possible values of x are 0, 1, 2, and 3. The values of the random value x are numerical.
C.The random variable is P(x), which is the probability of a number of girls in three births. The possible values of P(x) are 0.125 and 0.375. The values of the random value P(x) are numerical.
D.The random variable is x, which is the number of girls in three births. The possible values of x are 0, 1, 2, and 3. The values of the random value x are not numerical.
5. Ted is not particularly creative. He uses the pickup line “If I could rearrange the alphabet, I’d put U and I together.” The random variable x is the number of girls Ted approaches before encountering one who reacts positively. Determine whether the table describes a probability distribution. If it does, find its mean and standard deviation.
X P(x)
1 0.0020.002
2 0.0230.023
3 0.1340.134
4 0.2830.283
5 0.3190.319
Find the mean μ of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
μ = ________________ (Round to one decimal place as needed.)
The table is not a probability distribution.
Find the standard deviation σ of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
σ = ____________________ (Round to one decimal place as needed.)
The table is not a probability distribution.
6 Assume that a procedure yields a binomial distribution with n=55 trials and a probability of success of p=0.80 Use a binomial probability table to find the probability that the number of successes x is exactly 2.
See binomial probabilities table.
P (2) = ___________________ (Round to three decimal places as needed.)
7 Nine peas are generated from parents having the green/yellow pair of genes, so there is a 0.75 probability that an individual pea will have a green pod. Find the probability that among the 9 offspringpeas, at least 8 have green pods. Is it unusual to get at least 8 peas with green pods when 9 offspring peas aregenerated? Why or whynot?
The probability that at least 8 of the 9 offspring peas have green pods is _____________________________ (Round to three decimal places as needed.)
Is it unusual to randomly select 9 peas and find that at least 8 of them have a green pod? Note that a small probability is one that is less than 0.05.
A No, because the probability of this occurring is very small.
B. No, because the probability of this occurring is not small.
C. Yes, because the probability of this occurring is very small.
D. Yes, because the probability of this occurring is not small.
8 Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean μ and standard deviation σ. Also, use the range rule of thumb to find the minimum usual value mu minus 2 μ−2σ and the maximum usual value mu plus 2 μ+2σ.
n=220, p=0.75
μ = _________
σ = ______________ (Round to one decimal place as needed.)
μ−2σ = ________________ (Round to one decimal place as needed.)
μ+2σ = _________________ (Round to one decimal place as needed.)
9 A candy company claims that 12% of its plain candies are orange, and a sample of 200 such candies is randomly selected.
a. Find the mean and standard deviation for the number of orange candies in such groups of 200.
μ = _____________________
σ = ______________________ (Round to one decimal place as needed.)
b. A random sample of 200 candies contains 17orange candies. Is this resultunusual? Does it seem that the claimed rate of 12% is wrong?
A.Yes, because 17 is within the range of usual values. Thus, the claimed rate of 12 % is probably wrong.
B. Yes comma because 17 is greater than the maximum usual value. Thus, the claimed rate of 12% is probably wrong.
C. No comma because 17 is within the range of usual values Thus, the claimed rate of 12% is not necessarily wrong.
D. Yes comma because 17 is below the minimum usual value. Thus, the claimed rate of 12% is not necessarily wrong.
10 . For classes of 79 students, find the mean and standard deviation for the number born on the 4th of July. Ignore leap years.
b. For a class of 79 students, would two be an unusually high number who were born on the 4th of July?
a. The value of the mean is μ =___________ (Round to six decimal places as needed.)
The value of the standard deviation is σ = __________________ (Round to six decimal places as needed.)
b. Would 2 be an unusually high number of individuals who were born on the 4th of July?
A. No comma because 2 is within the range of usual values.
B. Yes comma because 2 is below the minimum usual value.
C.This result is unlikely because 2 is within the range of usual values.
D.Yes comma because 2 is greater than the maximum usual value.
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