Question

This Question: 1 pt 9 of 30 (complete This Test: 30 pts possibile o Theandem variatiews uniform distribution from 11 to 53 What is the probably the random variabile takes on a va that is within 12 standard deviations of the mean Round in the marettenth of a percent) OA 1495 OB 7165 OC.569 OD 676 OE. None of the above Type to search 8 5 6 7 8 9 Q E W R T Y P U A S А F G Н. J K L

Answer 1

We are given the distribution here as:

$X \sim U(a = 11, b = 53)$

Therefore the mean and standard deviation here are computed as:

$\mu = \frac{a + b}{2} = \frac{11 + 53}{2}= 32$

$\sigma = \frac{b - a}{\sqrt{12}} = \frac{53 - 11}{\sqrt{12}} = 12.1244$

The probability that the random variable lies within 1.22 standard deviations of the mean is computed here as:

P( 32 - 1.22*12.1244 < X < 32 + 1.22*12.1244)

= P(17.21 < X < 46.79)

= (46.79 - 17.21) / (53 - 11)

= 0.7043

Therefore 70.43% is the required probability here. Therefore E is the correct answer here.