Question

The variable x is normally distributed with a mean of 500 and a standard deviation of 50. Find a) The 60th percentile. b)The 35th percentile. c)The x value which exceeds 80% of all x values. d)The x value that is exceeded by 80% of all x values.

Answer 1

The answers are:

S.NO	Value	Condition
a)	512.667355	60th percentile
b)	480.733977	35th percentile
c)	542.081062	x value which exceeds 80%
d)	457.918938	x value that is exceeded by 80% of all x values.

a)

We need to find x such that P(X≤x) = 0.60

Pr(X≤x)=Pr(Z≤(x−500)/50​)=0.60

(x−500)/50 = 0.2533

> x = 512.667355

The following is obtained graphically:

b)

We need to find x such that P(X≤x) = 0.35

Pr(X≤x)=Pr(Z≤(x−500)/50​)=0.35

(x−500)/50 = −0.3853

>x=480.733977

The following is obtained graphically:

c)

We need to find x such that P(X≤x) = 0.80

Pr(X≤x)=Pr(Z≤(x−500)/50​)=0.80

(x−500)/50 = 0.8416

>x=542.081062

The following is obtained graphically:

d)

We need to find x such that P(X≤x) = 0.20

Pr(X≤x)=Pr(Z≤(x−500)/50​)=0.20

(x−500)/50 = −0.8416

>x=457.918938

The following is obtained graphically:

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