If you areexplicitly asked to express an answer as a percentage, to 2 decimal places for example, then a calculated probability of 0.24357 would need to have the answer entered as 24.36 (with NO percentage symbol entered). Where the questiondoesn'task you to express your answer as a percentage, enter it as a probability with a value between 0 and 1 (i.e. in the above example you would enter in the value of 0.2436 if the question stated to use 4 decimal places).

As instructed and demonstrated during the lectures and tutorials, youmustuse the textbookTable A.5(to find Z values and probabilities) andTable A.7(to find t values) to manually calculate the answers for this quizunless explicitly stated otherwise.Tables A.5 and A.7 are also available on Blackboard under the Learning Resources.Note that if a Z value is calculated and then used to find a probability, the Z value must be rounded to 2 decimal places first to use Table A.5.Only by using Table A.5 in this way will the correct probability be found to answer these quiz questions.For example, if your Z value is 2.7890, you must look up the Z value of 2.79 in Table A.5.

Note: Please noteno questions require you to use Kaddstat to calculate your final answer. Answers generated by Excel and Kaddstat may differ slightly to answers generated by the CML system (as the CML system is based on manual calculations). You mayhowever use Kaddstat to check the magnitude of your answers. If there is any discrepancy between your manually calculated answers and those given by Kaddstat (though both answers should typically be the same), please enter yourmanually calculated answers.

QUESTION 1

1. Courier Express wished to determine the average weight of parcels carried by its Brisbane operations. On the basis of historical data, the company was aware that the weight of parcels could be approximated by a normal distribution with a variance of0.472 kilograms squared. Last month, it weighed a random sample of15 parcels and found the average weight was 2.743 kg. Determine a 98% confidence interval for the average weight of parcels carried by Courier Express. State the lower limit of the interval (in kg), giving your answer to three decimal places.

3 points

QUESTION 2

1. A study on highway safety studied the driving habits of individuals. A sample of 74 carstravellingon the highway revealed an average speed of 102 kph with a standard deviation of 12.3 kph. Determine the critical value of the test statistic needed for a 95% confidence interval for the mean speed of all cars, if it is known that speed is normally distributed. Give the positive answer of the test statistic (z or t)exactly as found from tables (3 decimal places).

3 points

QUESTION 3

1. A market research company conducted a telephone survey of320 Melbourne households to determine the proportion of households seeking to purchase a new car in the next two years. An interval estimate of 0.134 to 0.196 was calculated. Determine the level of confidence (answer as percentage correct to two decimal places).

3 points

QUESTION 4

1. Sleep apnoea is a sleep disorder that causes a person to stop breathing momentarily and then awaken briefly. A study of763 Victorian commercial truck drivers found that 100 of them suffered from sleep apnoea. Use the survey results to estimate, with 90% confidence, the proportion of Victorian commercial truck drivers who suffer from this sleeping disorder. Report thelower bound of the interval only, giving your answer as a percentage to two decimal places.

2 points

QUESTION 5

1. A sales consultant for Herron Pharmaceuticals wished to confirm that their packet of 24 paracetamol tablets was cheaper at the retail level than their rival product. The sales consultant collected price data from two independent samples, of size19 for Herron and26 for the rival company. These yielded an average and variance for the retail price of Herron's product of351 cents and51 cents squared respectively, and362 cents and62 cents squared for the rival. Under the usual assumptions, determine an 80% confidence interval for the price difference (use Herron minus rival) stating only thelower limit of the interval in cents (round to the nearest whole number).

3 points

QUESTION 6

1. ANZ Bank's Wealth Management Division conducted a survey of the value of the new business created over the last month in millions of dollars. From 23 responses, the mean and standard deviation were found to be $3.129 and $0.534 million respectively. Assuming the data were collected through a random sample and that the value of new business is approximately normally distributed, calculate a 95% confidence interval estimate of the average value of new business per month in millions of dollars. State only the upper bound correct tothree decimal places.

2 points

QUESTION 7

1. Suppose that the duration of trouble-free operation of a new vacuum cleaner is normally distributed with a mean of 550 days and a standard deviation of 100 days. The research department randomly selects 25 customers who bought these vacuum cleaners and records the duration (in days) of trouble-free operation.Which of the following isNOTTRUEfor the sample average of number of trouble-free operation days ()?
2. P (x< 500) = P(Z < -2.5)
3. P(x> 600) = P(Z > 2.5)
4. P(x< 520) = P(Z < - 1.5)
5. P(550