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In a certain region, 10 percent of the homes have solar panels. A city official is...

In a certain region, 10 percent of the homes have solar panels. A city official is investigating energy consumption for homes within the region. Each week, the city official selects a random sample of homes from the region. Let random variable Y represent the number of homes selected at random from the region until a home that has solar panels is selected. The random variable Y has a geometric distribution with a mean of 10. Which of the following is the best interpretation of the mean?

A. Each week, the number of homes with solar panels increases by 10.

B. For a randomly selected week, it will take 10 homes before a home with solar panels is selected.

C. The average number of solar panels per home is equal to 10.

D. Over many weeks, the average number of homes with solar panels is 10.

E. Over many weeks, it takes 10 homes, on average, before a home with solar panels is selected.


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In a certain region, 10 percent of the homes have solar panels. A city official is investigating energy consumption for homes within the region. Each week, the city official selects a random sample of homes from the region. Let random variable Y represent the number of homes selected at random from the region until a home that has solar panels is selected. The random variable Y has a geometric distribution with a mean of 10. Which of the following is the best interpretation of the mean?

A. Each week, the number of homes with solar panels increases by 10.

Correct option: B. For a randomly selected week, it will take 10 homes before a home with solar panels is selected.

C. The average number of solar panels per home is equal to 10.

D. Over many weeks, the average number of homes with solar panels is 10.

E. Over many weeks, it takes 10 homes, on average, before a home with solar panels is selected.

Note: geometric distribution with a mean of 10. The mean of the geometric distribution is the expected number of trials required to get the first success, in this case it is 10.

orchestra answered 1 year ago
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