Question Continuation
Find the following probabilities. (Round your answers to four decimal places.)
(a) 15 or more will live beyond their 90th birthday
(b) more than 40 will live beyond their 90th birthday
Answer:
a. 0.9948
b. 0.0068
Step-by-step explanation:
Given
Number of graduating students, n = 723
Probability, p = 3.8% = 0.038
q = 1 - p = 1 - 0.038 = 0.962
Calculating the mean
Mean, u = np
u = 723 * 0.038
u = 27.474
Calculating the standard deviation
σ = √npq
σ = √(723 * 0.038 * 0.962)
σ = 5.14101040652516088641079
σ = 5.141 --- Approximated
We'll solve the following using z = (x-u)/σ
a.
x = 14.5 (I.e Atleast 15)
u = 27.474
σ = 5.141
Z = (14.5 - 27.474)/5.141
Z = −2.5236335343318420540750
Z = -2.52
From the binomial distribution table
The corresponding value at z = -2.52 is 0.0052
So, the probability that 15 or more will live beyond their 90th birthday = 1 - 0.0052
= 0.9948
b.
For more than 40
x = 40.5
u = 27.474
σ = 5.141
Z = (40.5 - 27.474)/5.141
Z = 2.53374829799649873565454
Z = 2.53
From the binomial distribution table
The corresponding value at z = 2.53 is 0.9932
So, the probability that more than 40 will live beyond their 90th birthday = 1 - 0.9932
= 0.0068
