Section 5.1

#5

Five males with anX-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit theX-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution isgiven, find its mean and standard deviation. If a probability distribution is notgiven, identify the requirements that are not satisfied.

x P(x)

0 0.034

1 0.157

2 0.309

3 0.309

4 0.157

5 0.034

Does the table show a probabilitydistribution? Select all that apply.

A.

Yes, the table shows a probability distribution.

B.

No, the random variablex's number values are not associated with probabilities.

C.

No, the sum of all the probabilities is not equal to 1.

D.

No, not every probability is between 0 and 1 inclusive.

E.

No, the random variable x is categorical instead of numerical.

Find the mean of the random variable x. Select the correct choice belowand, ifnecessary, fill in the answer box to complete your choice.

A.

=______child(ren) (Round to one decimal place asneeded.)

B.

The table does not show a probability distribution.

Find the standard deviation of the random variable x. Select the correct choice belowand, ifnecessary, fill in the answer box to complete your choice.

A.

= _______ child(ren) (Round to one decimal place asneeded.)

B.

The table does not show a probability distribution.

#7

A sociologist randomly selects single adults for different groups ofthree, and the random variable x is the number in the group who say that the most fun way to flirt is in person. Determine whether a probability distribution is given. If a probability distribution isgiven, find its mean and standard deviation. If a probability distribution is notgiven, identify the requirements that are not satisfied.

x P(x)

0 0.088

1 0.326

2 0.429

3 0.157

Does the table show a probabilitydistribution? Select all that apply.

A.

Yes, the table shows a probability distribution.

B.

No, the random variable x is categorical instead of numerical.

C.

No, the random variablex's number values are not associated with probabilities.

D.

No, not every probability is between 0 and 1 inclusive.

E.

No, the sum of all the probabilities is not equal to 1.

Find the mean of the random variable x. Select the correct choice belowand, ifnecessary, fill in the answer box to complete your choice.

A.

= ______ adult(s) (Round to one decimal place asneeded.)

B.

The table does not show a probability distribution.

Find the standard deviation of the random variable x. Select the correct choice belowand, ifnecessary, fill in the answer box to complete your choice.

A.

= ______adult(s) (Round to one decimal place asneeded.)

B.

The table does not show a probability distribution.

#8

The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls.

Number of Girls x P(x)

0 0.001

1 0.015

2 0.038

3 0.115

4 0.197

5 0.242

6 0.204

7 0.114

8 0.041

9 0.015

10 0.018

Use the range rule of thumb to identify a range of values that are not significant.

The maximum value in this range is _______girls.

(Round to one decimal place asneeded.)

#9

Refer to the accompanyingtable, which describes the number of adults in groups of five who reported sleepwalking. Find the mean and standard deviation for the numbers of sleepwalkers in groups of five.

Table of numbers of sleepwalkers and probabilities

x P(x)

0 0.176

1 0.357

2 0.297

3 0.134

4 0.033

5 0.003

The mean is ________sleepwalker(s). (Round to one decimal place asneeded.)

Section 5.2

#9

Assume that when adults with smartphones are randomlyselected, 59% use them in meetings or classes. If 12 adult smartphone users are randomlyselected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.

The probability is ______.

(Type an integer or decimal rounded to four decimal places asneeded.)

#12

The probability of a randomly selected adult in one country being infected with a certain virus is 0.002. In tests for thevirus, blood samples from 24 people are combined. What is the probability that the combined sample tests positive for thevirus? Is it unlikely for such a combined sample to testpositive? Note that the combined sample tests positive if at least one person has the virus.

The probability that the combined sample will test positive is _______.

(Round to three decimal places asneeded.)

#13

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 51 tablets, then accept the whole batch if there is only one or none thatdoesn't meet the required specifications. If one shipment of 4000 aspirin tablets actually has a 3% rate ofdefects, what is the probability that this whole shipment will beaccepted? Will almost all such shipments beaccepted, or will many berejected?

The probability that this whole shipment will be accepted is _______.

(Round to four decimal places asneeded.)