Homework Answers

At the beginning of the first day (day 1) after grape harvesting is completed, a grape grower has 8000 kg of grapes in storage. On day n, for n = 1, 2, . . . , the grape grower sells 250n/(n + 1) kg of the grapes at the local market at the price of $2.50 per kg. He leaves the rest of the grapes in storage where each day they dry out a little so that their weight decreases by 3%. Let wn be the weight (in kg) of the stored grapes at the beginning of day n for n ≥ 1 (before he takes any to the market).

(a) Find the value of wn for n = 2.

(b) Find a recursive definition for wn. (You may find it helpful to draw a timeline.)

(c) Let rn be the total revenue (in dollars) earned from the stored grapes from the beginning of day 1 up to the beginning of day n for n ≥ 1. Find a recursive formula for rn.

Suppose that the bank customers arrive randomly and independently on an average of 3.2

customers every 4 minutes. What is the probability that:

a. Exactly two customers arrive in every 4 minutes?

At a certain college, it is estimated that approximately 19% of the students ride bicycles to school. Would you consider this to be valid estimate if, in a random sample of 85 college students, 20 are found to ride bicycles to class

A random sample of 20 drinks from a soft-drink machine has an average content of 21.9 deciliters, with a standard deviation of 1.42 deciliters. At 0.05 level of significance, test the hypothesis that μ = 22. 2 against the alternative hypothesis μ < 22.2. Assume that the distribution is normal.

A researcher claims that 13% of all motorcycle helmets have manufacturing flaws that could potentially cause injury to the wearer. A sample of 150 of these helmets revealed that 18 contained such defects.

A random sample of 20 drinks from a soft-drink machine has an average content of 21.9 deciliters, with a standard deviation of 1.42 deciliters. At 0.05 level of significance, test the hypothesis that μ = 22. 2 against the alternative hypothesis μ < 22.2. Assume that the distribution is normal.

Your given ∑ 𝑥 = 44 , ∑ 𝑥2 = 174, ∑ 𝑥𝑦 = 1324, in addition you also given the values of y

as:

Y 26 28 24 18 35 24 36 25 31 37 30 32

3a. calculate the Pearson correlation coefficient [7]

3b. estimate the y value associated with x=4 [8].

3c. You are given the mean of 20.3 for a random sample of 90 observations from a normal distribution population with a standard deviation of 3.9. Construct a 95% confidence level and interpret your answer. [3]