Topic: Central Limit Theorem Suppose that you are a student worker in the Mathem
ID: 3173203 • Letter: T
Question
Topic: Central Limit Theorem
Suppose that you are a student worker in the Mathematics Department and they agree to pay
randomly. Each week the Chair flips a fair coin. Your pay for the week is $80 if it comes up heads,
and your pay is $40 if it comes up tails. Your friend is working for another department and makes
$62 a week.
(a) Estimate the probability that your total earnings in 100 weeks are more than hers.
(b) If you compare your earnings over 50 weeks instead of 100 weeks, would the above mentioned
probability increase or decrease?
Explanation / Answer
Mean of pay during week = (1/2)80+(1/2)40 = 60
variance = (1/2)(40-60)2 +(1/2)(80-60)2 = 400
standard devaition = 20
a)
mean for 100 weeks = 100*60 = 6000
standard deviation for 100 weeks = 100*20/100 = 200
z value for 6200 is (6200-6000)/200 = 1,pvalue = 0.841345
P(my payment <her payment in 100 weeks ) = P(X<6200) = 0.841345
probability that your total earnings in 100 weeks are more than hers = 1- P(X<6200) = 1- 0.841 = 0.159
b)standard deviation for 50 weeks = 50*2050 = 141.42
z value will be more in this case
P(my payment <her payment in 50 weeks ) > P(my payment <her payment in 100 weeks )
P(my payment >her payment in 50 weeks ) < P(my payment >her payment in 100 weeks )
so probailty will decrese for 50 weeks than 100 weeks