BAmD216 chapter6 QUESTION 1 1. The assembly time for a product is uniformly dist

Question

BAmD216

chapter6

QUESTION 1

1.      The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability of assembling the product in less than 6 minutes is

5 points   

QUESTION 2

1.      Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. The probability that x will take on a value of at least 26 is

5 points   

QUESTION 3

1.      The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. The mean time is

2.5 points   

QUESTION 4

1.      The advertised weight on a can of soup is 10 ounces. The actual weight in the cans follows a uniform distribution and varies between 9.3 and 10.3 ounces. Compute the standard deviation of the weight of a can of soup.

2.5 points   

QUESTION 5

1.      Z is a standard normal random variable. The P(1.41 <= z <=2.85) equals

5 points   

QUESTION 6

1.      For a standard normal distribution, the probability of obtaining a z value of more than 1.6 is

5 points   

QUESTION 7

1.      Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.1401?

5 points   

QUESTION 8

1.      The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?

5 points   

QUESTION 9

1.      The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. The probability of a player weighing more than 241.25 pounds is

5 points   

QUESTION 10

1.      The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. What percent of players weigh between 180 and 220 pounds?

5 points   

QUESTION 11

1.      The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.  What is the minimum weight of the top 2% of players?

5 points   

QUESTION 12

1.      The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. The highest 15% of MBA graduates earns what minimum salary ?

Explanation / Answer

1) Let X be the random variable that assembly time.

X ~ uniform (6,10)

Here we have to find P(X<6).

The pdf of X is,

f(x) = 1 / 10-6 = 1/4 , for 6 <=X<=10

P(X<6) = f(x) dx over 0 to 6

But we have define pdf for  6 <=X<=10 and for x<6 and x > 10 pdf is 0.

P(X<6) = 0

2) X ~ Uniform(20, 28)

Here we have to find P(X>=26).

The pdf of X is,

f(x) = 1/8, 20 <=X <=28

P(X>=26) = f(x) dx for 26 <=X<=28

= 1/8 dx   for 26 <=X<=28

= 1/8 1 dx   for 26 <=X<=28

= 1/8 [x] for 26 <=X<=28

= 1/8 [ 28-26 ] = 2 / 8 = 0.25

3) Let X be that random variable that the travel time for a college student traveling between her home and her college.

X ~ Uniform(40, 90)

Mean time = (40 + 90) / 2 = 65

4) Let X be the actual weight in the cans.

X ~ Uniform(9.3, 10.3)

standard deviation = sqrt ( (10.3-9.3)2 / 12) = 0.2887

5) Z is a standard normal random variable.

The P(1.41 <= z <=2.85) = P(Z <=2.85) - P(Z <=1.41) = 0.9978 - 0.9207 = 0.0771

6) For a standard normal distribution, the probability of obtaining a z value of more than 1.6 is

P(Z > 1.6) = 1 - P(Z<=1.6) = 1 - 0.9452 = 0.0548

7) Let X be the random variable that the starting salaries of individuals with an MBA degree.

X ~ Normal(mean = 40000, sd=5000)

And we have to find P(X>=30000).

First here we have to find z-score for x=30000.

z = (x-mean) / sd

z = (30000 - 40000) / 5000 = -2

P(Z > -2) = 1 - P(Z <=-2) = 1 - 0.0228 = 09772

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