07 Jan No comma because 2 is
Homework 2
1. Heights of men on a baseball team have a? bell-shaped distribution with a mean of 183 cm and a standard deviation of 7 cm. Using the empirical? rule, what is the approximate percentage of the men between the following? values?
a. 162 cm and 204 cm
b. 176 cm and 190 cm
a. _________of the men are between 162 cm and 204 cm.
?(Round to one decimal place as? needed.)
b. _____of the men are between 176 cm and 190 cm.
?(Round to one decimal place as? needed.)
2. Cans of regular soda have volumes with a mean of 12.72 oz and a standard deviation of 0.11 oz. Is it unusual for a can to contain 13.1 oz of? soda?
Minimum? “usual”
?(Type an integer or a? decimal.)
Maximum? “usual
?(Type an integer or a? decimal.)
Is 13.1 oz an? “unusual” volume?
A.
Yes comma because it is larger than the maximum “usual” value.
.B.
?Yes, because it is smaller than the minimum? “usual” value.
C.
?No, because it is smaller than the minimum? “usual” value.
D.
No comma because it is between the minimum and maximum “usual” values.
E.
?Yes, because it is between the minimum and maximum? “usual” values.
F.
?No, because it is larger than the maximum? “usual” value.
3.Five males with a particular genetic disorder have one child each. The random variable x is the number of children among the five who inherit the genetic disorder. Determine whether the table describes a probability distribution. If it? does, find the mean and standard deviation.
x
0
1
2
3
4
5
?P(x)
0.00210.0021
0.02510.0251
0.12290.1229
0.30100.3010
0.36850.3685
0.1804
Find the mean of the random variable x. Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice.
A.
muequals
B.
The table is not a probability distribution.
Find the standard deviation of the random variable x. Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice.
A.
sigmaequals
1.0 ?(Round to one decimal place as? needed.)
B.
The table is not a probability distribution.
4. Heights of women have a? bell-shaped distribution with a mean of 156 cm and a standard deviation of 8 cm. Using? Chebyshev’s theorem, what do we know about the percentage of women with heights that are within 3 standard deviations of the? mean? What are the minimum and maximum heights that are within 3 standard deviations of the? mean?
At least ______ of women have heights within 3 standard deviations of 156 cm.
?(Round to the nearest percent as? needed.)
The minimum height that is within 3 standard deviations of the mean is _________cm.
The maximum height that is within 3 standard deviations of the mean is ________cm.
5. The accompanying table describes results from eight offspring peas. The random variable x represents the number of offspring peas with green pods. Complete parts? (a) through? (d).
Probabilities of Numbers of Peas with Green Pods Among 8 Offspring Peas
x (Number of Peas with Green Pods)
P(x)
0
0+
1
0+
2
0.0030.003
3
0.0290.029
4
0.0840.084
5
0.1740.174
6
0.3620.362
7
0.2570.257
8
0.0910.091
a. Find the probability of getting exactly 7 peas with green pods.
b. Find the probability of getting 7 or more peas with green pods.
c. Which probability is relevant for determining whether 7 is an unusually high number of peas with green? pods, the result from part? (a) or part? (b)?
The result from part? (a)
The result from part? (b)
d. Is 7 an unusually high number of peas with green? pods? Why or why? not? Use 0.05 as the threshold for an unusual event.
A.
?No, since the appropriate probability is greater than? 0.05, it is not an unusually high number.
B.
?No, since the appropriate probability is less than? 0.05, it is not an unusually high number.
C.
?Yes, since the appropriate probability is less than? 0.05, it is an unusually high number.
D.
?Yes, since the appropriate probability is greater than? 0.05, it is an unusually high number.
6. Determine whether the given procedure results in a binomial distribution. If it is not? binomial, identify the requirements that are not satisfied.
Recording the genders of 50 people in a statistics class nothing
Choose the correct answer below.
A.
No comma because there are more than two possible outcomes.
B.
Yes comma because all 4 requirements are satisfied.
C.
?No, because the probability of success does not remain the same in all trials.
D.
?No, because there are more than two possible outcomes and the trials are not independent.
7. Fifteen 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 15 offspring? peas, no more than 1 has a green pod. Is it unusual to get no more than 1 pea with a green pod when 15 offspring peas are? generated? Why or why? not?
The probability that no more than 1 of the 15 offspring peas has a green pod is ___
?(Round to three decimal places as? needed.)
Is it unusual to randomly select 15 peas and find that no more than 1 of them have a green? pod? Note that a small probability is one that is less than 0.05.
A.
Yes?, because the probability of this occurring is very small.
B.
No?, because the probability of this occurring is very small.
C.
No?, because the probability of this occurring is not small.
D.
Yes?, because the probability of this occurring is not small.
8. A brand name has a 50?% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 5 randomly selected consumers. Complete parts? (a) through? (d) below.
a. What is the probability that exactly 4 of the selected consumers recognize the brand? name?
The probability that exactly 4 of the 5 consumers recognize the brand name is _______?(Round to three decimal places as? needed.)
b. What is the probability that all of the selected consumers recognize the brand? name?
The probability that all of the selected consumers recognize the brand name is ________?(Round to three decimal places as? needed.)
c. What is the probability that at least 4 of the selected consumers recognize the brand? name?
The probability that at least 4 of the selected consumers recognize the brand name is ____?(Round to three decimal places as? needed.)
d. If 5 consumers are randomly? selected, is 4 an unusually high number of consumers that recognize the brand? name?
A.
Yes?, because the probability that 4 or more of the selected consumers recognize the brand name is greater than 0.05.
B.
No?, because the probability that 4 or more of the selected consumers recognize the brand name is greater than 0.05.
C.
Yes?, because the probability that 4 or more of the selected consumers recognize the brand name is less than 0.05.
D.
No?, because the probability that 4 or more of the selected consumers recognize the brand name is less than 0.05.
9. 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 mu and standard deviation sigma. ?Also, use the range rule of thumb to find the minimum usual value mu minus 2 sigma and the maximum usual value mu plus 2 sigma.
nequals1450?, pequals3/5
mu=
sigma=
mu minus 2 sigma=
mu plus 2 sigma =
10. a. For classes of 166 ?students, find the mean and standard deviation for the number born on the 4th of July. Ignore leap years.
b. For a class of 166 ?students, would two be an unusually high number who were born on the 4th of? July?
a. The value of the mean is mu=
?(Round to six decimal places as? needed.)
The value of the standard deviation is sigma=
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 greater than the maximum usual value.
C.
Yes comma because 2 is below the minimum usual value.
D.
This result is unlikely because 2 is within the range of usual values.
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