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Question 2. A normal random variable x has mean $\mu = 15$ and standard deviation $\sigma = 3$. a. Find $P(15.4 < x < 16.5)$. b. Find $P(x > 16.5)$

          Question 2.
A normal random variable x has mean $\mu = 15$ and standard deviation $\sigma = 3$.
a. Find $P(15.4 < x < 16.5)$.
b. Find $P(x > 16.5)$
        
Question 2.
A normal random variable x has mean μ = 15 and standard deviation σ = 3.
a. Find P(15.4 < x < 16.5).
b. Find P(x > 16.5)

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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A normal random variable x has a mean μ = 15 and standard deviation σ = 3. a. Find P(15.4 < x < 16.5). b. Find P(x > 16.5).
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Transcript

-
00:01 In this problem, we are given that there is a random variable x, and this is having normal distribution, such that the mean of the distribution is 15, and the standard deviation, well, that's given as 4 .4.
00:15 And we have to find the probability that x is greater than 16 .5.
00:20 So here we will first use this formula, and we will compute the z score corresponding to the data value 16 .5.
00:28 So when we plug in the values of the variables, along with the value of x as 16 .5, we will get the z score here as 16 .5 minus 15 over 4 .4, which comes out to be 0 .341...
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