A) The sign on the elevator in the Peters Building, which houses the School of Business and Economics at WLU, states, 'Maximum Capacity 1,140...
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Question

# A) The sign on the elevator in the Peters Building, which houses the School of Business and Economics at WLU,

states, "Maximum Capacity 1,140 kilograms (2,500 pounds) or 16 Persons." A professor of statistics wonders what the probability is that 16 persons would weigh more than 1,140 kilograms. Discuss what the professor needs (besides the ability to perform the calculations) in order to satisfy his curiosity.

B) Refer to Exercise Suppose that the professor discovers that the weights of people who use the elevator are normally distributed with an average of 75 kilograms and a standard deviation of 10 kilograms. Calculate the probability that the professor seeks.

Exercise

The sign on the elevator in the Peters Building, which houses the School of Business and Economics at WLU, states, "Maximum Capacity 1,140 kilograms (2,500 pounds) or 16 Persons." A professor of statistics wonders what the probability is that 16 persons would weigh more than 1,140 kilograms. Discuss what the professor needs (besides the ability to perform the calculations) in order to satisfy his curiosity.

C) The time it takes for a statistics professor to mark his midterm test is normally distributed with a mean of 4.8 minutes and a standard deviation of 1.3 minutes. There are 60 students in the professor's class. What is the probability that he needs more than 5 hours to mark all the midterm tests? (The 60 midterm tests of the students in this year's class can be considered a random sample of the many thousands of midterm tests the professor has marked and will mark.)

D) Refer to Exercise Does your answer change if you discover that the times needed to mark a midterm test are not normally distributed?

Exercise

The time it takes for a statistics professor to mark his midterm test is normally distributed with a mean of 4.8 minutes and a standard deviation of 1.3 minutes. There are 60 students in the professor's class. What is the probability that he needs more than 5 hours to mark all the midterm tests? (The 60 midterm tests of the students in this year's class can be considered a random sample of the many thousands of midterm tests the professor has marked and will mark.)

E) The restaurant in a large commercial building provides coffee for the occupants in the building. The restaurateur has determined that the mean number of cups of coffee consumed in a day by all the occupants is 2.0 with a standard deviation of .6. A new tenant of the building intends to have a total of 125 new mployees. What is the probability that the new employees will consume more than 240 cups per day?

F) The number of pages produced by a fax machine in a busy office is normally distributed with a mean of 275 and a standard deviation of 75. Determine the probability that in 1 week (5 days) more than 1,500 faxes will be received?

Date :
Page No.:
TELCO!
The professor requires an idea about
the weights of the people who use
that elevator I's . a distribution .
Let x be the weight of such aperson
given X V N ( 7 5 10 2 )
Let...

IX: Time required to mark one test
Given X N N ( 4 . 8 , 1 . 3 2 )
Y = EX = Time required to mark to test
YN N ( 60 ( 4 . 8 ) , 60 ( 1 . 3 ) 2 )
Pr [ y &gt; 5 hrs ] = Pr [ y 7 30 0 minutes ]
= \ Pr...

Date :
Page No.:
TELCO!
OF)| x : no of pages produced per day
L
Given , X N N ( 2 7 5, 75 2 )
No . of pages in I week ( 5 days )
= X + X + . .+ X = 5X - y (say)
14375
. . ; ; E X = 5 X = y N N ( 5...

NOTES
Date :
Page No.:
TELCO!
Let X, X, . In be normally distrim
i'd [ independently s identically distributed
random variables
such as
Xi ~ N ( u , 5 2 )
for ald i = 1 .
Then Let Y = . E X , N N (...

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