2. A sample of 100 is selected from a population with mean µ =100 and ? = 20.0.
(a) Describe the sampling distribution of the sample meanX¯.
(b) Find P(X >¯ 105).
(c) Find P(100 < X <¯ 105).
(d) Find P(98 < X <¯ 104).
3. According to the U.S. Department of Energy, the average priceof unleaded regular gasoline sold at service stations throughoutthe nation is $1.23 per gallon with a standard deviation of $0.16.A random sample of 45 stations is selected and the pump prices forunleaded gasoline are recorded. Find the probability that thesample mean price:
(a) exceeds $1.28 per gallon,
(b) is less than $1.19 per gallon,
(c) is between $1.20 and $1.27 per gallon,
4. Almost all medical schools in the U. S. require students totake the Medical College Admission Test (MCAT). Suppose that thetest scores follow a normal distribution with mean 25.0 andstandard deviation 6.5.
(a) One student is selected at random, what is the probabilitythat the student’s score is between 20 and 30?
(b) A random sample of 36 students is selected, what is theprobability that their mean score is between 20 and 30?
