1)A variableXhas a mean of 73.5 and a standard deviation of 61.4. A random sample of size 30 is selected. AssumingXis 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

Part BTrue or False:

It was necessary to assume that the variableXis normally distributed in part (a) of this question.Answer by placing T or F in the space provided.

2)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.xxData can be copied and pasted intoExcelto complete the calculations.

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

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 lowerand upper limits of the confidence interval? Give your answers to one decimal place, in the form xxx.x

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.