please answer completely and correctly all questions thanks CIS3300 Business Ana

Question

please answer completely and correctly all questions thanks

CIS3300 Business Analytics Quiz # 3 1. The life expectancy in the United States is 75 with a standand deviation of 7 years a. What is the probability that a randomly selected U.S resident will be older than 77 years at the time of death? b. What is the probability that the individual's age is precisely 72,.7 years at the time of death? What is the probability that the individual's age will be 65 years or younger at the time of death? c. d. Up to what age can an individual expect to live with a 90% probability?

Explanation / Answer

mean = 75
std. dev. = 7

a)
As per central limit theorem, z = (xbar - mu)/sigma

P(X > 77)
= P(z > (77 - 75)/7)
= P(z > 0.2857)
= 0.3875
(Excel function used to calculate =1-NORM.DIST(0.2857,0,1,TRUE))

b)
P(X = 72.7)
= P(z = (72.7 - 75)/7)
= P(z = -0.3286)
= 0.378
(Excel function used to calculate =NORM.DIST(-0.3286,0,1,FALSE))

c)
P(X < 65)
= P(z < (65 - 75)/7)
= P(z < -1.4286)
= 0.0766
(Excel function used to calculate =NORM.DIST(-1.4286,0,1,TRUE))

d)
z-value respective to 90% probability is 1.2816 (=NORM.INV(0.9,0,1))

Using central limit theorem
xbar = 75 + 1.2816*7 = 83.9712

Hence life expectancy with 90% probability is 84 years.

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