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STATS -Problems on Normal Distribution

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Question;Directions: Draw a clearly labeled diagram and then solve each problem.;1. The gestation period (length of pregnancy) for male babies born in New York is normally distributed with a mean of 39.4 weeks and a standard deviation of 2.43 weeks.;(a) What percent of mothers of male babies are pregnant for less than 35 weeks?;(b) What percent of mothers of male babies are pregnant for between 35 and 40 weeks?;(c) What percent of mothers of male babies are pregnant for more than 40 weeks?;(d) Suppose a sailor had shore leave 46 weeks ago and his wife is delivering a baby today. What should the sailor say to his wife when he gets home?;2. Suppose that a school district wants to start a program for gifted students. The participants in the program are to be chosen on the basis of IQ scores (normal withm = 100,s = 15). If the school district wants only the top 2% of students to participate in the program, what should be the IQ score that students must exceed to be accepted?;3. The daily demand for gas at Good?s Gas station is normally distributed with a mean of 1812 gallons and a standard deviation of 254 gallons.;(a) What is the probability that the demand for gas will exceed 2000 gallons on any day?;(b) What is the probability that the demand for gas in a day will be between 1500 and 2000 gallons?;(c) What is the probability that the demand for gas will exceed 1500 gallons on any day?;d) how much gasoline should the station have on hand at the beginning of the day so that the probability of running out of gas that day is only 1%?;4. 10% of Americans are left handed.;(a) If 6 people are selected at random, what is the probability that more than 3 of them are left-handed?;(b) Suppose a group of 600 mathematicians get together for a conference. What is the probability that more than 80 of them are left-handed? (Use the normal approximation to the binomial);5. Airlines sell more tickets for a flight than the number of available seats (overbooking). They do this because they know from past experience that only 90% of ticketed passengers actually show up for the flight. A plane has 325 seats. If the airline sells 350 tickets for a flight, what is the probability that the flight will be overbooked (the number of passengers who show up is greater than the number of available seats)?;6. The mean pulse rate for adults is 72 beats per minute (www.healthepic.com) and let?s suppose that the standard deviation is 10. Find;a. The probability that a randomly chosen adult has a pulse rate over 80 assuming that the rates are normally distributed.;b. The probability that a random sample of 19 adults will have a mean pulse rate over 80.

 

Paper#62377 | Written in 18-Jul-2015

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