1 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. Question 2 1. Duracell Ltd claim that the life of their batteries in motorised soft toys is approximately normally distributed with a mean of 92.3 hours and a standard deviation of 15.7 hours. The worst 9% of batteries would not last beyond how many hours? Answer correct to 2 decimal places. Question 3 1. The general manager of a logistic consulting group believes that 34% of the firm's orders come from new customers. A simple random sample of 96 orders was taken. Assuming that the manager's claim is correct, determine (to 4 dec pl): 1. the standard error for the sampling distribution of proportion. 2. 2. the probability that no more than 28% of the sample orders will be from new customers. Question 4 1. Fortune 500 Magazine claimed that the average age of a US CEO was 58.3 years with a standard deviation of 4.8 years. If a random sample of 55 US CEOs were taken, what is the probability that the sample mean will lie within two years of the average age claimed by the magazine? Give your answer as a percentage correct to one decimal place. Question 5 1. Strategic business planning is required for the successful transfer of control between generations in family-owned companies. However, a survey of 356 privately held family firms whose annual turnover exceeded one million dollars it was found that 90 had no strategic business plan. Assuming that simple random sampling was employed to determine the sample for the survey, estimate with 95% confidence the PROPORTION of family-owned companies operating without strategic business plans. Give the upper limit only and report your answer correct to three decimal places. Question 6 1. An interval estimate for the average distance "lifetime" for car tyres was reported to be 32468 kilometres to 37224 kilometres, based on a sample of 48 tyres. The variance of the lifetime was determined from previous studies to be 44582179 kms sqd. What level of confidence can be attributed to this interval estimate? State your answer as a percentage correct to two decimal places. Question 7 1. The weight of the contents of a can of Campbell's minestrone soup can be modelled by a normal distribution with a mean of 439.9 grams and a standard deviation of 3.2 grams. A random sample of 15 cans is selected for quality control testing. Determine the probability that (4 dec pl) 1. a randomly selected can weighs more than 437.5 grams, 2. the sample mean of the cans taken for quality control testing will NOT be within the target range of 438.0 to 442.0 grams. Question 8 1. A recent study measured the amount of time a physician took with her patients. From the study it was determined that the time was normally distributed with a mean of 15 minutes and a standard deviation of 2 minutes. The probability that the doctor will spend between 10 and 12 minutes is 0.0555 2. 0.0606 0.340 0.4623