4. The diameters of apples in a certain orchard are normally distributed with a mean of 5.55 inches and a standard deviation of 0.65 inches. Show all work.
(A) What percentage of the apples in this orchard has diameters less than 5.8 inches?
(B) What percentage of the apples in this orchard is larger than 6.3 inches?
5. Assume that the average annual salary for a worker in the United States is $27,500 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,250. Find the following:
(A)What percentage of Americans earn below $18,000?
(B)What percentage of Americans earn above $40,000?
7. Answer the following:
(A) Find the binomial probability P(x = 5), where n = 12 and p = 0.30.
(B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation.
(C) How would you find the normal approximation to the binomial probability P(x = 5) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations.
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