In each situation below, is it reasonable to use a binomial distribution for the
ID: 3124746 • Letter: I
Question
In each situation below, is it reasonable to use a binomial distribution for the random variable X? Give reasons for your answer in each case. (a) A random sample of students in a fitness study. X is the mean systolic blood pressure of the sample. Yes, a binomial distribution is reasonable. X can only take on two values. No, a binomial distribution is not reasonable. X is not a count of successes. No, a binomial distribution is not reasonable. Binomial distributions cannot be used with random samples. No, a binomial distribution is not reasonable. X should be associated with a population. Yes, a binomial distribution is reasonable. X is a mean of the binomial distribution. (b) A manufacturer of running shoes picks a random sample of the production of shoes each day for a detailed inspection. Today's sample of 20 pairs of shoes includes 1 pair with a defect. No, a binomial distribution is not reasonable. One defect in a sample of 20 is not a large enough percentage. No, a binomial distribution is not reasonable. Binomial distributions cannot be used with random samples. Yes, a binomial distribution is reasonable. p is the probability of a defective pair. Yes, a binomial distribution is reasonable. p is the number of defective shoes from today's sample. No, a binomial distribution is not reasonable. One defect is not a large enough count. (c) A nutrition study chooses an SRS of college students. They are asked whether or not they usually eat at least five servings of fruits or vegetables per day. X is the number who say that they do. Yes, a binomial distribution is reasonable. n is the number of students chosen from the sample and X is the number of servings of fruits and vegetables they eat. No, a binomial distribution is not reasonable. A student might eat less than five servings of fruits and vegetables but could claim otherwise. Yes, a binomial distribution is reasonable. p is the percentage of students chosen from the population and n is the number of servings of fruits and vegetables they eat. Yes, a binomial distribution is reasonable. n is the number of students in the sample and p is the probability that a student eats at least five servings of fruits and vegetables. No, a binomial distribution is not reasonable. Binomial distributions cannot be used with random samples.
Explanation / Answer
a) A random sample of students in a fitness study. X is the mean systolic blood pressure of the sample.
Ans : No, a binomial distribution is not reasonable. X is not a count of successes.
(b) A manufacturer of running shoes picks a random sample of the production of shoes each day for a detailed inspection. Today's sample of 20 pairs of shoes includes 1 pair with a defect.
Ans : Yes, a binomial distribution is reasonable. p is the probability of a defective pair.
(c) A nutrition study chooses an SRS of college students. They are asked whether or not they usually eat at least five servings of fruits or vegetables per day. X is the number who say that they do.
Ans : Yes, a binomial distribution is reasonable. n is the number of students in the sample and p is the probability that a student eats at least five servings of fruits and vegetables.