Question

Assume that X has a normal distribution, and find the indicated probability.

The mean is μ = 15.2 and the standard deviation is σ = 0.9.

Find the probability that X is between 14.3 and 16.1.

Group of answer choices

0.6826

0.8413

0.3413

0.1587

Answer 1

Solution:
Given in the question
Mean(μ) = 15.2
Standard deviation(σ ) = 0.9
We need to calculate probability that X is between 14.3 and 16.1 which can be calculated as
P(14.3<X<16.1) = P(X<16.1) - P(X<14.3)
Here we will use standard normal distribution table, first we will calculate Z-score which can be calculated as
Z-score = (X-μ)/σ = (16.1-15.2)/0.9 = 1
Z-score = (X-μ)/σ = (14.3-15.2)/0.9 = -1
From Z table we found p-value
P(14.3<X<16.1) = P(X<16.1) - P(X<14.3) = 0.8413 - 0.1587 = 0.6826
So there is 68.26% probability that X is between 14.3 and 16.1.