1.The life of cell batteries is normally distributed with a mean of 84.9 hours and a standard deviation of18.5 hours.93% of the batteries will last more than how many hours?(2 decimal places )

2.Fortune 500 Magazine claimed the average age of all US Chief Executive Officers (CEOs) was 58.3 years with a standard deviation of 4.8 years. If a random sample of 55 USCEOswas selected, find theprobabilitythat the sample mean will lie within 2 years of the average age claimed by the magazine? Give your answer to three decimal places.

3.The length of time for long-distance phone calls has been found to be normally distributed, with a mean of 24.4 minutes and a standard deviation of5.5 minutes. In a randomly selected sample of56 calls, what is the sample average call time below which 10% of sample average call times will be shorter? (2 decimal places)

4)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 15.2 minutes and a variance of 12.34 minutes².

a)Find the probability that a consultation would last more than 12.5 minutes.

b)How many of the individual patients visiting the medicalcentrewill have a consultation time of more than 12.5 minutes if there are 553 individual patient consultations on a given day?Use your roundedanswer, with 3 decimal places, from part a.

5)Which of the following is false?

A.The standard normal distribution has a mean of zero and a variance of one.

B.The standard normal distribution is useful because any normally distributed variable can be converted to the standard normal.

C.The standard normal distribution is useful because it has a smaller variance than other normal distributions.

D.The standard normal distribution hasprobability values already tabulated.

6)A study measured the amount of consultation time physicians took with patients. From the study, it was determined that the consultation time was normally distributed with a mean of 15 minutes and a standard deviation of 2 minutes.What is the probability that the doctor will spend more than 11 minutes? Select from the answers below.

1. 0.9772
2. 0.4330
3. 0.0228
4. 0.4772

7)The marketing manager for the print division of Publishing and Broadcasting Limited claims that 27% of university students regularly read the Bulletin magazine. A survey of 95 students showed that 35 students actually read the Bulletin regularly. Assuming the manager's claim is correct, determine (to 4 decimal places):

1.the standard error for the sampling distribution of the proportion.

2. the probability that the sample proportion could be at least that found in the survey.

8)Benford's Law is a probability rule frequently used by accounting auditors to detect systematic fraud. It states that approximately 16.6% of numbers will begin with the number 2.An auditor decides to investigate a particular firm further if a sample proportion of their invoices, with the invoiced number beginning with a 2, is in the highest 0.5% of all possible sample proportions.What sample proportion will cause further investigation of the firm if a random sample of 542 invoices is selected? Express youranswer in decimal form (ienot as a percentage),correct to two decimal places.

9)GIL internet services record customer usage patterns.Historically they have found the duration of an internet session is normally distributed with an average duration of 77.5 minutes and a standard deviation of 20.6 minutes.What is the probability a randomly selected session would last longer than twohours or less than thirty-five minutes? (4 decimal places)

10) The weight of the contents of a can of Campbell's minestrone soup can be modelled by a normal distribution with a mean of 440.8 grams and a standard deviation of 3.7 grams. A random sample of 18 cans is selected for quality control testing. Determine the probability that (to 4 decimal places)

1. A randomly selected can weighs less than 435.0 grams or more than 445.0 grams

2. The sample mean of the cans will exceed 442.0 grams.