Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of u = 1.1 kg and a standard deviation of = 5.1 kg. Complete parts (a) through (c) below.

a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year.

The probability is ____. Round to four decimal places as needed.

 

b. If 4 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.

The probability is ____. (Round to four decimal places as needed.)

 

c. Why can the normal distribution be used in part (b) even though the sample size does not exceed 30?

◯ A. Since the original population has a normal distribution. the distribution of sample means is a normal distribution for any sample size

◯ B. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.

◯ C. Since the weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size.

◯ D. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.

Problem 2 (7 points) Bags of chips are marked with a weight of 40 ounces. The weight of the bags actually varies according to a normal distribution with mean = 40 ounces and standard deviation=1.8 ounces. If a bag is selected at random, what is the probability that it actually weighs more than 42 ounces?

A set of 10 cards consists of five red cards and five black cards. The cards are shuffled thoroughly. 12. Six of these cards will be selected at random. Let X = the number of red cards observed in the set of six selected cards. Which of the following probability distributions is appropriate for modeling the random variable X? A) The Normal distribution with mean 3 and variance 1.22. B) The binomial distribution with parameters n= 6 and p=0.5. C) The binomial distribution with parameters n = 10 and p = 0.5. D) None of the above.

During the summer months, the prices of nonsmoking rooms with a king-size bed in hotels in a certain area are roughly Normally distributed with a mean of $131.80 and a standard deviation of $29.12. 5. A travel agent randomly selects prices of nonsmoking rooms with a king-size bed from 15 hotels in the area. What is the probability that their average cost will be more than $150? A) 0.0077 B) 0.1125 C) 0.2660 D) 0.3678