Question 4

As a part of the productivity assessment at a company, the HR Manager carried out a survey and

found that inclusive of overtime the amount of time spent at work per week follows a normal

distribution with ?=47 hours and ? 2 ? 4.

a. Calculate the P(X?43)

b. Determine the probability that the length of the work week is between 45 and 55

hours.

Problem Set 2 This worksheet covers material from units 3-5. It contributes 8% to your final grade and is due on Saturday November 19, 2016 at 11:55 PM EC time/ 10:55 PM JA time. Please show all working and/or explanation. Please submit assignment in the dropbox provided in the learning exchange. No late assignment will be accepted and no assignment will be accepted via email. Question 1 A random sample of 80 persons was taken and they were asked if they are in favour of or against capital punishment. The following table gives the two way classification of their responses. Male Favours Capital Punishment 32 Opposes capital punishment 24 Female 13 11 If an individual is selected: a. What is the probability that the person is a male? b. What is the probability that the individual is a female and favours capital punishment? c. What is the probability that the individual is female given that he/she opposes capital punishment? Question 2 The following table is the probability distribution for cash prizes in a lottery conducted at a local department store. Prize ($) 0 10 100 500 Probability 0.45 0.30 0.20 0.05 a. If you buy a single ticket, what is the probability that you win no more than $100? b. Compute the mean and standard deviation of the distribution Question 3 A manufacturer of window frames knows from past experience that 10 per cent of the production will have some type of minor defect that will require adjustment. Suppose 30 windows are selected at random: a. How many window frames would you expect to have minor defects? b. What is the probability that more than 3 window frames will need minor adjustments? Question 4 As a part of the productivity assessment at a company, the HR Manager carried out a survey and found that inclusive of overtime the amount of time spent at work per week follows a normal distribution with =47 hours and 2 4 . a. Calculate the P(X43) b. Determine the probability that the length of the work week is between 45 and 55 hours. Question 5 The scores on a test are normally distributed with a mean of 100 and a standard deviation of 25. Forty scores were randomly selected. a. Determine the sampling distribution of the mean for the sample. b. What is the probability that the mean is more than 102? c. What is the probability that the mean is less than 100? Question 6 A recent survey of 50 unemployed male executives showed that it took a mean of 26 weeks to find another position. The standard deviation was 6.2 weeks. a. Construct a 95% confidence interval for the mean time it will take executives to find another job. b. Briefly interpret the interval constructed in part (a) above. Question 7 The credit manager at a bank wants to find out whether the mean monthly unpaid balance is more than $400. A random check of 172 unpaid balances revealed a sample mean of $407 and a standard deviation of $38. The credit manager want to determine if the population mean is greater than $400? a. State the null and alternate hypotheses. b. What is the test statistic to be used? c. Using the 5% level of significance, should the credit manager conclude that the population mean is greater than $400? Question 8 Based on a study conducted last year, the incidence of heavy drinking among teenagers was 15%. You are in charge of monitoring this rate and conducted the annual survey. Of the 234 teenagers in the survey, 40 of them were heavy drinkers. If you want to know if the incidence rate has changed a. What are the null and alternate hypotheses? b. What is the test statistic to be used? c. Using a 5% significance level, can we conclude that the incidence rate has changed? Problem Set 2 This worksheet covers material from units 3-5. It contributes 8% to your final grade and is due on Saturday November 19, 2016 at 11:55 PM EC time/ 10:55 PM JA time. Please show all working and/or explanation. Please submit assignment in the dropbox provided in the learning exchange. No late assignment will be accepted and no assignment will be accepted via email. Question 1 A random sample of 80 persons was taken and they were asked if they are in favour of or against capital punishment. The following table gives the two way classification of their responses. Male Favours Capital Punishment 32 Opposes capital punishment 24 Female 13 11 If an individual is selected: a. What is the probability that the person is a male? b. What is the probability that the individual is a female and favours capital punishment? c. What is the probability that the individual is female given that he/she opposes capital punishment? Question 2 The following table is the probability distribution for cash prizes in a lottery conducted at a local department store. Prize ($) 0 10 100 500 Probability 0.45 0.30 0.20 0.05 a. If you buy a single ticket, what is the probability that you win no more than $100? b. Compute the mean and standard deviation of the distribution Question 3 A manufacturer of window frames knows from past experience that 10 per cent of the production will have some type of minor defect that will require adjustment. Suppose 30 windows are selected at random: a. How many window frames would you expect to have minor defects? b. What is the probability that more than 3 window frames will need minor adjustments? Question 4 As a part of the productivity assessment at a company, the HR Manager carried out a survey and found that inclusive of overtime the amount of time spent at work per week follows a normal distribution with =47 hours and 2 4 . a. Calculate the P(X43) b. Determine the probability that the length of the work week is between 45 and 55 hours. Question 5 The scores on a test are normally distributed with a mean of 100 and a standard deviation of 25. Forty scores were randomly selected. a. Determine the sampling distribution of the mean for the sample. b. What is the probability that the mean is more than 102? c. What is the probability that the mean is less than 100? Question 6 A recent survey of 50 unemployed male executives showed that it took a mean of 26 weeks to find another position. The standard deviation was 6.2 weeks. a. Construct a 95% confidence interval for the mean time it will take executives to find another job. b. Briefly interpret the interval constructed in part (a) above. Question 7 The credit manager at a bank wants to find out whether the mean monthly unpaid balance is more than $400. A random check of 172 unpaid balances revealed a sample mean of $407 and a standard deviation of $38. The credit manager want to determine if the population mean is greater than $400? a. State the null and alternate hypotheses. b. What is the test statistic to be used? c. Using the 5% level of significance, should the credit manager conclude that the population mean is greater than $400? Question 8 Based on a study conducted last year, the incidence of heavy drinking among teenagers was 15%. You are in charge of monitoring this rate and conducted the annual survey. Of the 234 teenagers in the survey, 40 of them were heavy drinkers. If you want to know if the incidence rate has changed a. What are the null and alternate hypotheses? b. What is the test statistic to be used? c. Using a 5% significance level, can we conclude that the incidence rate has changed