Question

Assume the random variable X is normally distributed with meanmu equals 50μ=50and standard deviationsigma equals 7σ=7.Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.Upper P left parenthesis 34 less than Upper X less than 63 right parenthesisP(34

Answer 1

Answer: 0.9575465

Explanation:

Let the random variable X is normally distributed with mean
`\mu=50` and standard deviation
`\sigma=7` .

Using the formula ,
`z=(x-\mu)/(\sigma)` , we have the z-value for x= 34

`z=(34-50)/(7)\approx-2.29`

For x= 63

`z=(63-50)/(7)\approx1.86`

P-value : P(34<x<63)=P(-2.29<z<1.86)

`=P(z<1.86)-P(z<-2.29)\\\\=0.9685572-(1-P(z<2.29))\\\\1=0.9685572-(1-0.9889893)\\\\=0.9575465`

Hence, the required probability = 0.9575465