Question 9 The time taken to thoroughly audit the books of a small business by Royce, Smith and Jones Auditors has been

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Question 9 The time taken to thoroughly audit the books of a
small business by Royce, Smith and Jones Auditors has been found to
follow a normal distribution with a mean of 5.8 days and a standard
deviation of 7 days. For what proportion of claims is the
processing time expected to be longer than 8 days? Give your answer
to two decimal places in the form 0.xx.
Answer: Answer
Part B The company is currently auditing the books of 40 small
businesses. How many, to the nearest whole number are expected to
take longer than 8 days to audit? Give your answer in the form xx
or x as appropriate.
Answer: Answer
Question 10 In this question, use Excel functions rather than
Normal distribution tables. The number of new cars sold by "Ma's
New Car Factory" in a financial year can be approximated by a
normal distribution with a mean of 125,000 cars and a standard
deviation of 35,000 cars. Part A In order to recover all costs
associated with manufacture they need to sell 100,000 cars. What is
the probability that "Ma's New Car Factory" will do better than
just covering their costs if the sales are distributed as expected?
Give your answer to two decimal places in the form x.xx. Answer:
Answer
Part B What is the number of cars sales that the company has a
only a 10% chance of achieving next year? Give you answer as a
whole number. Answer: Answer
Question 11 Suppose X~N(55,45.5). {Remember that this means
Normally distribut(mean, standard deviation)} In part B of this
exercise you will be required to find P(X<105) using tables.
Part A Find the value z0 of the standard normal variable Z, such
that P(X < 105) = P(Z < z0) Give your answer to 2 decimal
places in the form x.xx or -x.xx as appropriate.
z0 = Answer
Part B Use tables to find the probability P(X < 105). Give
your answer rounded to 2 decimal places in the form 0.xx
Probability: Answer
Question 12 If X is a random variable with a mean of 84.43 and a
standard deviation of 17.23, what is the mean of the sample means
calculated from samples of size 12 drawn from this population? Give
your answer to two decimal places in the form xx.xx Answer:
Answer
Question 13 If X is a random variable with a mean of 71.52 and a
variance of 140.23, what is the mean of the sample means calculated
from samples of size 7 drawn from this population? Give your answer
to two decimal places in the form xx.xx
Answer: Answer
Part B And what is the standard error of the mean? Give your
answer to two decimal places in the form x.xx or xx.xx as
appropriate.
Answer: Answer
Question 14 A variable X has a mean of 73.5 and a standard
deviation of 61.4. A random sample of size 30 is selected. Assuming
Xis normally distributed, what is the probability, to two decimal
places, that the sample mean exceeds 100? Give your answer to two
decimal places in the form x.xx
Answer: Answer
Part B True or False: It was necessary to assume that the
variable X is normally distributed in part (a) of this question.
Answer by placing T or F in the space provided.
Answer: Answer
Question 15 13011303In a survey conducted to determine the costs
of holidays, 196 individuals were randomly sampled. Each was asked
to assess the total cost of his or her most recent holiday. The
average cost was $1386. Part A Assuming that the population
standard deviation was $500, estimate the population mean cost of
holidays with 99% confidence. Give the lower and upper limits of
this confidence interval to the nearest whole number of dollars in
the form xxxx (Do not include a dollar sign.) Lower limit: Answer
Upper limit: Answer
Part B What is the width of the confidence interval? Give your
answer to the nearest whole number. Width: Answer Part C True or
false: The width of a 95% confidence interval would be larger.
Answer by placing T or F in the space provided.
Answer: Answer
Question 16 406.3Part A Market researchers want to estimate the
mean monthly expenditure on transport for households in Sydney.
They randomly selected 19 householders and asked their expenditure
on transport, in dollars, over the past month. Data from the
selected households are given below.
181
266
339
292
420
150
484
488
282
571
536
153
583
434
135
187
497
144
520 What is the best point estimate of the population mean, to
two decimal places? Give your answer in the form xxx.xx Data can be
copied and pasted into Excel to complete the calculations.
Answer: Answer
Part B Now assume that the population standard deviation is
known to be 170. To two decimal places, what is the standard error
for the mean of the sample? Give your answer in the form xx.xx
Answer: Answer
Part C Based on the given sample and the known standard
deviation, calculate a 90% confidence interval for mean monthly
expenditure on transport. What are the lower and upper limits of
the confidence interval? Give your answers to one decimal place, in
the form xxx.x Lower limit: Answer Upper limit: Answer Part D True
or false: A 99% confidence interval based on the same sample would
be narrower. To answer, type T or F in the space provided.