# Probability and Statistics

## Question 8: The current advertising campaign for a major soft drink brand would be changed if less than 30 percent of consumers like it. a) Formulate the null and alternative hypothesis b) Discuss the Type land Type II errors that could occur in hypothesis testing. c) Which statistical test would you use? Why? d) A random sample of 300 consumers was surveyed, and 84 respondents indicated that they liked the campaign. Should the campaign be changed? Why?

EXPERT ANSWER a) Ho : p = 0.3H1 : p < 0.3 b) Type I error is concluding that less than 30% of custimers like it while in actual it equal or greater than 30% Type I error is concluding that equal to or greater than 30% of custimers like it while in actual it …

## Assume that a substation transformer has a constant hazard rate of 0.005 per day. What is the probability that it will fail during the next 5 years? What is the probability that it will not fail?

Assume that a substation transformer has a constant hazard rate of 0.005 per day. What is the probability that it will fail during the next 5 years? What is the probability that it will not fail? EXPERT ANSWER

## A manufacturer makes ball bearing that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually less than 30g the mean weight for a random sample of 16 ball bearings is 28.6 g with a standard deviation of 4.4 g. At the 0.05 significance level these the claim that the sample comes from a population with a mean weight less than 30 g. Use the traditional method of testing hypothesis.

A manufacturer makes ball bearing that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually less than 30g the mean weight for a random sample of 16 ball bearings is 28.6 g with a standard deviation of 4.4 g. At the 0.05 significance level these …

## 4. (15 points) When a fair coin is tossed, 2 points are scored if a head is obtained and 5 points are scored if a tail is obtained. Suppose the coin is tossed three times and let the random variable X be the total score obtained. (a) What are the possible values of X? (b) What is the probability mass function of X? (c) What is the cumulative distribution function of X? (d) What is the expected value and standard deviation of X?

EXPERT ANSWER Q4) a) X is the total number of points that can be obtained here. There are 4 possible combinations here for 3 tosses:All heads where we get: 3*2 = 6 points2 heads and 1 tails: 2*2 + 5 = 9 points1 head and 2 tails: 2 + 5*2 = 12 points3 tails: 15 …