Question

Suppose that NoP(X5)6 and P(X 2):2 find P( 3< X < 4).

Answer 1

Solution:-

8) P( 3 < X < 4) = 0.0679

P(x > 5) = 0.60

x = 5

p-value for the X > 5 is = 1 - 0.60 = 0.40

z-score for the p-value = - 0.253

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

$\mu -0.253\ast \sigma =5$.......................(1)

P(x < 2) = 0.20

x = 2

p-value for the X < 2 is = 0.20

z-score for the p-value = - 0.842

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

$\mu -0.842\ast \sigma =2$....................(2)

By solving equation (1) and (2) we get

$\mu =6.29,\sigma =5.09$

x₁ = 3

x₂ = 4

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

z₁ = - 0.646

z₂ = - 0.449

P( - 0.647 < z < -0.449) = P(z > -0.647) - P(z > -0.449)

P( - 0.647 < z < -0.449) = 0.7412 - 0.6733

P( - 0.647 < z < -0.449) = 0.0679