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1. Suppose the time to...

1. Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds. Suppose that to qualify for the Nationals, a woman must complete the 200-meter backstroke in less than 128 seconds. What proportion of competitive female swimmers will qualify for the Nationals? Give your answer to four (4) decimal places.2. Suppose the scores on an exam are normally distributed with a mean μ = 75 points and standard deviation σ = 8 points.What is the exam score for an exam whose z-score is 1.25?65

75

85

0.8944

0.10563. Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds.Suppose the fastest 6% of female swimmers in the nation are offered college scholarships. In order to be given a scholarship, a swimmer must complete the 200-meter backstroke in no more than how many seconds? Give your answer in whole numbers.5. The number of days (X) after mailout it takes a utility company to receive payment for a customer’s bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days.The probability is 0.997 that a bill will be received between which of the following number of days?(13, 49)

(19, 43)

(25, 37)6. According to the Bureau of Labor Statistics, in May 2014 the mean hourly wage of a social worker was $28.08 with a standard deviation of $1.97. Jeronica is a social worker with an hourly wage of $31.60. What is Jeronica’s z-score? (Round your answer to 2 decimal places.)7. The time it takes a surgeon to complete a laproscopic surgery to remove the gall bladder is normally distributed with a mean of 132.4 minutes and a standard deviation of 15.7 minutes. A patient’s risk of complications is increased the longer he is in surgery. An unusually risky surgery is one that is in the top 4% of all surgery lengths.What is the minimum surgery length (in minutes) that would be considered unusually risky? Note: Answers are rounded to 1 decimal place.247.4 minutes

147.5 minutes

159.9 minutes

104.9 minutes

75

85

0.8944

0.10563. Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds.Suppose the fastest 6% of female swimmers in the nation are offered college scholarships. In order to be given a scholarship, a swimmer must complete the 200-meter backstroke in no more than how many seconds? Give your answer in whole numbers.5. The number of days (X) after mailout it takes a utility company to receive payment for a customer’s bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days.The probability is 0.997 that a bill will be received between which of the following number of days?(13, 49)

(19, 43)

(25, 37)6. According to the Bureau of Labor Statistics, in May 2014 the mean hourly wage of a social worker was $28.08 with a standard deviation of $1.97. Jeronica is a social worker with an hourly wage of $31.60. What is Jeronica’s z-score? (Round your answer to 2 decimal places.)7. The time it takes a surgeon to complete a laproscopic surgery to remove the gall bladder is normally distributed with a mean of 132.4 minutes and a standard deviation of 15.7 minutes. A patient’s risk of complications is increased the longer he is in surgery. An unusually risky surgery is one that is in the top 4% of all surgery lengths.What is the minimum surgery length (in minutes) that would be considered unusually risky? Note: Answers are rounded to 1 decimal place.247.4 minutes

147.5 minutes

159.9 minutes

104.9 minutes

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