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I’m working on a economics question and need an explanation and answer to help me learn.

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A market research firm wishes to estimate the proportion of personal computers sold this year by

relatively unknown manufacturers.

(a) (3 points) This firm specifies that the estimation of this proportion has a margin of error 0.03

with 95% confidence. Find the smallest sample size required.

(b) (3 points) Later on this firm finds out that 30% of the personal computers sold last year came

from relatively unknown manufacturers. This firm uses this further information, and also specifies

that the estimation of this year’s proportion be within 0.03 with 95% confidence. Find the smallest

sample size required.

(c) (3 points) The firm ignores the sample sizes in (a) and (b) above. The firm selects a random sample

of 1,000 personal computers sold this year, and the sample shows that 400 of them come from

relatively unknown manufacturers. Find a 95% confidence interval for the real proportion.

Two instruments A and B are designed to measure v, the speed a rocket. Measurements from

instrument A follow a normal distribution with mean v and standard deviation 0.006v.

Measurements from Instrument B follow a normal distribution with mean v and standard deviation

0.004v. Instrument A has made 3 measurements and their average value is X, and instrument B has

made 3 measurements and their average is Y.

a

(a) (5 points) Suppose measurements from instruments A and B are independent. What is the

probability that the average value of X and Y is within 0.005v of the speed v? Hint: the average

value of X and Y is (X+Y)/2.

(b) (5 points) Suppose measurements from instruments A and B are not independent, and the

correlation coefficient between X and Y is 0.2. What is the probability that the average value of X

Cand Y is within 0.005v of the speed v? Hint: the average value of X and Y is (X+Y)/2.

A survey conducted in year 2021 suggested that 210 out of 300 (70 percent) of university students

worked in the summer of 2021. A similar survey is planned for year 2022. Researchers believe that

the 70 percent fraction will remain unchanged. They wish to construct a 90 percent confidence

interval for the difference in proportions and wish to ensure a margin of error at 5 percent. Find the

required sample size for the 2022 survey.

Suppose the frequency distribution of customer satisfaction rating are given below:

Rating

Frequency

1

300

2

450

3

200

4

50

Total

1000

A random sample of 400 viewers is selected from this population. Assume that their ratings are

independent from each other.

(a) (5 points) What is the probability that at least 120 customers in this sample will give a rating 3 or

4?

(b) (5 points) What is the probability that the average rating from this sample is higher than 2.1?

A truck can carry a maximum load of 10,000 kilograms. A manufacturer wants to ship an order of 64

boxes. Suppose the average weight of a box is 155 kilograms with standard deviation 25 kilograms.

(a) (5 points) What is the probability that all 64 boxes can be sent in one shipment?

(b) (5 points) Suppose this truck will be upgraded to increase its maximum load so that 90 percent

of the times, all 64 boxes can be sent in one shipment. What is the upgraded maximum load?

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Explanation & Answer:

400 words

Tags:

math

economics

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