STAT 4.10-12 Binomial Prob Dist

According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor’s degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor’s degree. What is the probability that B will equal 40 ?

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According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor’s degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor’s degree. What is the probability that B will equal 14 or less ?

• 50.7%

• 24.7%

• 38.7%

• 59.3%

• 65.2%

According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor’s degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor’s degree. What is the probability that B will equal 20 or more ?

• 6.6%

• 0.01%

• 3.55%

• 19.3%

• 10.2%

According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor’s degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor’s degree. What is the probability that B will equal 16 ?

• 13.6%

• 8.9%

• 3.55%

• 19.3%

• 11.9%

According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor’s degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor’s degree. What is the probability that B will equal 15 ?

• 13.6%

• 12.1%

• 3.55%

• 19.3%

• 11.9%

A large store has a customer service department where customers can go to ask for help with store-related issues. According to store records, approximately ¼ of all customers who go to the service department ask for help finding an item. Assume the reason each customer goes to the service department is independent from customer to customer. Based on the approximation, what is the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item?

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A blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contains the tap water. Assuming that people cannot taste a difference between bottled water and tap water, what is the probability that at least 8 of the 9 participants will correctly identify the tap water?

• 0.0020

• 0.0195

• 0.8889

• 0.9805

• 0.0351

In a certain region, 94 percent of the people have a certain characteristic in their blood. Suppose a group of 45 people from the region are selected at random. Let the random variable B represent the number of people in the sample without the characteristic. Random variable B follows a binomial distribution with a mean of 2.7 people. Which of the following is the best interpretation of the mean?

• For all groups of 45 people, the average number of people without the characteristic is 2.7.

• Every group of 45 people will have 2.7 people with the characteristic.

• Every group of 45 people will have 2.7 people without the characteristic.

• On average, 2.7 people are selected until finding someone with the characteristic.

• On average, 2.7 people are selected until finding someone without the characteristic.

In a certain region, 94 percent of the people have a certain characteristic in their blood. Suppose a group of 45 people from the region are selected at random. Let the random variable B represent the number of people in the sample without the characteristic. Random variable B follows a binomial distribution with a mean of 2.7 people. What is the probability of selecting more than 4 out of 45 who have the characteristic in their blood?

• 13.1%

• 25.1%

• 50.3%

• 1.2%

• 6.2%

In a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). The probability of rolling doubles with one roll of two fair six-sided dice is 1/6.

What is the probability that it takes three rolls until the player rolls doubles?

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