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 is a mean of the binomial distribution. No, a binomial distribution is not reasonable. Binomial distributions cannot be used with random samples. Yes, a binomial distribution is reasonable. x can only take on two values. No, a binomial distribution is not reasonable. X should be associated with a population. O 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. No, a binomial distribution is not reasonable. Binomial distributions cannot be used with random samples. No, a binomial distribution is not reasonable. One defect is not a large enough count. O Yes, a binomial distribution is reasonable. p is the probability of a defective pair ONo, a binomial distribution is not reasonable. One defect in a sample of 20 is not a large enough percentage. O Yes, a binomial distribution is reasonable. p is the number of defective shoes from today's sample (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. JX is the number who say that they do. No, a binomial distribution is not reasonable. Binomial distributions cannot be used with random samples. OYes, 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 O Yes, a binomial No, a binomial distribution is not reasonable. A student might ea less than five servings of fruits and vegetables but could claim otherwise. eat. 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. distribution is reasonable. ρ is the percentage of students chosen rom the population and n is the number of servings of fruits and vegetables Yes, a binomial they eat.

Answer 1

A. Last option is correct as binomial considers the counts of successes in independent binary trials.

B. Third option is correct with p as the probability of a defective pair.

C. Third option is correct with n as the size of the sample and p as the probability of eating atleast 5 vegetables.