Question

(a) Given a standard normal distribution, find the area under the curve that lies between

z = −0.48 and z = 1.74.

(b) Find the value of z if the area under a standard normal curve between 0 and z, with

z > 0, is 0.4838.

(c) Given a normal distribution with μ = 30 and σ = 6, find the two values of x that

            contains the middle 75% of the normal curve area.

Answer 1

This is a normal distribution question with


a)
z1 = -0.48
z2 = 1.74
This implies that

Since, we have to find the z value corresponding to the values between z = 0 and P(Z=z) = 0.4838
NOw, we will add P(Z=0) = 0.5 to P(Z=z) = 0.4838
to get a p = 0.9838

b) Given in the question
P(X < x) = 0.9838
This implies that

Therefore, now we can say P(0 < z < 2.14) = 0.4838

c)
This is a normal distribution question with

we need to find teh middle 75% which is between
p = (1-0.75)/2 = 0.125 and p = 1 - (1-0.75)/2 = 1 - 0.125 = 0.875

Given in the question, p = 0.125
P(X < x) = 0.125
This implies that
P(Z < -1.1503) = 0.125
With the help of formula for z, we can say that



Given in the question,p = 0.875
P(X < x) = 0.875
This implies that
P(Z < 1.1503) = 0.875
With the help of formula for z, we can say that

23.0982 & 36.9018 contain 75% of the normal curve

PS: you have to refer z score table to find the final probabilities.
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