QUESTION 1

1. A firm produces cans of soup.The can weights are normally distributed with a mean of 451 grams and a standard deviation of 13 grams.
2. a) If a single can is randomly selected during a production run, find the probability the can weight is less than 438 grams.(4 decimal places)b) The quality control inspector randomly selects a sample of 42 cans for testing.Find the probability that the sample average weight will be more than 455 grams.(4 decimal places)

4 points

QUESTION 2

1. A study was conducted to determine the duration of a typical consultation in an urban medical practice.The results showed that the length of a consultation could be closely approximated by a normal distribution with a mean of 14.2 minutes and a variance of 10.37 minutes².
2. a)Find the probability that a consultation would last less than 12 minutes.(3 decimal places)
3. b)How many of the individual patients visiting the medical centre will have a consultation time of less than 12 minutes if there are 412 individual patient consultations on a given day?
4. Use your rounded answer, with 3 decimal places, from part a.(Round your answer to the nearest whole number.)

4 points

QUESTION 3

1. An on-line retailing firm conducts a study into the number of on-line purchases of footwear made during all of last year.The study wants to determine the proportion of Australians over the age of 25 who purchase footwear on-line. The managing director of the on-line retailing firm believes this proportion of Australians is 18%. A random sample of 103 Australians over the age of 25 is selected. If the managing director's claim is true, what is the sample proportion value below which 10% of all sample proportions would exist? Express your answer correct to two decimal places.

3 points

QUESTION 4

1. The general manager of a distributor business believes that 25% of the firm's orders come from new or first-time customers. A simple random sample of 174 orders will be used to estimate the proportion of new or first-time customers. Find the probability that the sample proportion will be between 0.22 and 0.33. Give answer correct to 4 decimal places.

3 points

QUESTION 5

1. Duracell ltd claim that the life of their batteries in motorised soft toys is approximately normally distributed with a mean of 100.6 hours and a standard deviation of 16.5 hours. The worst 12% of batteries would not last beyond how many hours? Answer correct to 2 decimal places.

2 points

QUESTION 6

1. The average and standard deviation of the amount of Goods and Services tax remitted by performance artists in a twelve month period were $7.825 thousand and $1.764 thousand respectively. If a sample of 105 artists was chosen, find the sample average value above which only 15% of sample averages would lie. Give your answer in dollars (to the nearest dollar).

2 points

QUESTION 7

1. Which of the following is false?
2. The sampling distribution of the sample proportion is the distribution of values of the sample proportion from all possible samples of size n drawn from a population.When a sample proportion is calculated, the population from which the sample comes is discrete.The variance of the sample proportion is equal to the variance of a binomial random variable divided by the sample size squared.The sampling distribution of the sample proportion is approximately normally distributed provided the population is normally distributed.

2 points

QUESTION 8

1. AMART has monitored the duration of calls to its customer service line over a long period and found the duration of calls can bemodelledas a normal distribution with a true mean of 5.76 minutes and a standard deviation of 1.41 minutes.What probability of calls last between 3 and 7 minutes? Give your answer to 4 decimal places.

2 points

QUESTION 9

1. The marks on a midterm test are normally distributed with a mean of 65 and a standard deviation of 12. Find the probability that a class of 25 has an average mark that is more than 70. (3 dec places)

4 points

QUESTION 10

1. Bags of potting mix have weights that follow a normal distribution with an average weight of 20 kg and a standard deviation of 2.7 kg. Find the weight below which only 9% of the bags are lighter:

1. 16.3799 kg
2. 13.6128 kg
3. 16.382 kg
4. 23.62 kg