Review problems1. The scores on an admission test the Engineering Program of a certain university arenormally distributed with a mean of 500 and a standard deviation of 100.a) What is the probability that a randomly selected student will obtain a score of morethan 605?b) What is the score that separates the top 33% from the lower 67%?c) What is the probability that the average score of a random sample of 9 studentswill be more than 605?d) Why is a sample size of 9 sufficient for the solution in part c to be valid?2. In a survey to estimate the proportion of Canadians favoring the introduction of anew federal law, a random sample of 400 Canadians resulted in 216 in favor of theintroduction of the new law.a) Find a 90% CI for the true proportion of Canadians favoring the introduction of thelaw.b) What is the interpretation of the confidence interval in (a)?c) Would a 99% confidence interval be wider or narrower than the 90% confidenceinterval of (a)?d) How large a sample would have to be taken to estimate the proportion favoring thenew law to within 0.05 with 94%?3. A courier service advertises that its average delivery time is less than 6 hours for localdeliveries. A random sample of times for 50 deliveries across town gave a mean of 5.87and a standard deviation of 1.02.a) Test whether the sample results support the courier’s advertisement. Useα= 0.05.b) What assumption did you make in answering part (a)?4. In the television commercial, the manufacturer of toothpaste claims that more than4 out of 5 dentists recommend the ingredients in his product.To test this claim, aconsumer-protection group randomly sampled 400 dentists and asked each one whetherthey would recommend toothpaste that contained the ingredients. 329 of the dentistsanswered “yes” and 71 answered “no”. At the 0.05 level of significance, is there enoughevidence to support the manufacturer’s claim?5. The manager of a large bank wishes to estimate the average savings account balance.The bank’s accountant takes a random sample os 121 of the accounts and finds a meanaccount balance of $473.25 with a variance of $11449.0.a) Find a 95% confidence estimate for the true mean savings account balance.