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(solution) Please answer the following question showing step by step works.


Please answer the following question showing step by step works.


Problems on Normal Distribution

 

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. (a) 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.

 

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? 3. Suppose that the life of an Evercharged battery is normally distributed with a mean

 

life of 12 hours and a standard deviation of 0.72 hours. What percent of Evercharged

 

batteries will last:

 

a) less than 11.5 hours

 

b) more than 13 hours

 

c) between 11.5 and 13 hours? 4. 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

 

with = 100, = 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? 5. In problem #2, 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%? 6. 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) 7. If a couple has five children, what is the probability that :

 

(a) they have three boys and two girls (b) all five are boys

 

more than 3 boys (c) at least one is a girl (d) they have 8.In a redundant communications network, there are 6 paths between two nodes, so that if a message can not get

 

through one path, it can be sent through one of the other paths. Suppose that the probability that an individual path

 

is busy is 80%. What is the probability that a message can be sent from one node to the other?

 


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