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In Exercises 6鈥�10, use the following: Five American Airlines flights are randomly selected, and the table in the margin lists the probabilities for the number that arrive on time (based on data from the Department of Transportation). Assume that five flights are randomly selected.

Find the mean of the number of flights among five that arrive on time.

In Exercises 7鈥�14, determine whether a probability

distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.

Five males with an X-linked genetic disorder have one child each. The random variable xis the number of children among the five who inherit the X-linked genetic disorder.

a.The probability of 7 hurricanes in a year is equal to 0.140.

b. Thus, the expected number of years to have 7 hurricanes in a 55-year period is equal to 7.7 years.

c. The expected number of years that have 7 hurricanes is approximately equal to the actual number of years that have 7 hurricanes in a 55-year period.Since the expected and the actual values are approximately equal, the Poisson distribution works well here.

In Exercises 6鈥�10, use the following: Five American Airlines flights are randomly selected, and the table in the margin lists the probabilities for the number that arrive on time (based on data from the Department of Transportation). Assume that five flights are randomly selected.

Based on the table, the standard deviation is 0.9 flight. What is the variance? Include appropriate units.

In Exercises 7鈥�14, determine whether a probability

distribution is given. If a probability distribution is given, find its mean and standarddeviation. If a probability distribution is not given, identify the requirements that are not satisfied.

When conducting research on color blindness in males, a researcher forms random groups with fivemales in each group. The random variable xis the number of males in the group who have a form of color blindness (based on data from the National Institutes of Health).

Identifying Binomial Distributions. In Exercises 5鈥�12, determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not binomial, identify at least one requirement that is not satisfied.

LOL In a U.S. Cellular survey of 500 smartphone users, subjects are asked if they find abbreviations (such as LOL or BFF) annoying, and each response was recorded as 鈥測es,鈥� 鈥渘o,鈥� or 鈥渘ot sure.鈥�

Groups of people aged 15鈥�65 are randomly selected and arranged in groups of six. The random variable xis the number in the group who say that their family and / or partner contribute most to their happiness (based on a Coca-Cola survey). The accompanying table lists

the values of xalong with their corresponding probabilities. Does the table describe a probability distribution? If so, find the mean and standard deviation.

In Exercises 6鈥�10, use the following: Five American Airlines flights are randomly selected, and the table in the margin lists the probabilities for the number that arrive on time (based on data from the Department of Transportation). Assume that five flights are randomly selected.

What does the probability of 0+ indicate? Does it indicate that among five randomly selectedflights, it is impossible for none of them to arrive on time?

In Exercises 7鈥�14, determine whether a probability

distribution is given. If a probability distribution is given, find its mean and standarddeviation. If a probability distribution is not given, identify the requirements that are notsatisfied.

Ted is not particularly creative. He uses the pickupline 鈥淚f I could rearrange the alphabet, I鈥檇 put U and I together.鈥漈he random variable xis the number of women Ted approachesbefore encountering one who reacts positively.

Detecting FraudThe Brooklyn District Attorney鈥檚 office analyzed the leading (leftmost) digits of check amounts in order to identify fraud. The leading digit of 1 is expected to occur 30.1% of the time, according to 鈥淏enford鈥檚 law,鈥� which applies in this case. Among 784 checks issued by a suspect company, there were none with amounts that had a leading digit of 1.

a. If there is a 30.1% chance that the leading digit of the check amount is 1, what is the expected number of checks among 784 that should have a leading digit of 1?

b. Assume that groups of 784 checks are randomly selected. Find the mean and standard deviation for the numbers of checks with amounts having a leading digit of 1.

c. Use the results from part (b) and the range rule of thumb to identify the values that are significantly low.

d. Given that the 784 actual check amounts had no leading digits of 1, is there very strong evidence that the suspect checks are very different from the expected results? Why or why not?