Question

In: Statistics and Probability

The distribution of ages of all the employees in Company X follows a normal distribution. The...

The distribution of ages of all the employees in Company X follows a normal distribution. The average age is 40 and the standard deviation is 5.

Find the Z-score of a 50 year old employee.

What is the probability that a randomly chosen employee will be younger than 35 years?

What is the probability that a randomly chosen employee will have an age between 35 and 45 years?

What is the probability that a randomly chosen employee will be older than 55 years?

Find the Z-score of a 35 year old employee.

Solutions

Expert Solution

Solution :

Given that ,

mean =   = 40

standard deviation = = 5   

a.using z score formula

z =(X- ) / = 50 -40 / 5=2

b.

P(X< 35) = P[(X- ) / < (35-40) /5 ]

= P(z < -1)

Using z table

= 0.1587

c.

P(35< x <45 ) = P[(35 - 40) /5 < (x - ) / < (45 - 40) / 5)]

= P(-1< Z <1 )

= P(Z < 1) - P(Z < -1)

Using z table   

= 0.8413-0.1587

probability= 0.6826

d.

P(x > 55) = 1 - P(x< 55)

= 1 - P[(x -) / < (55-40) /5 ]

= 1 - P(z <3 )

Using z table

= 1 - 0.9987

= 0.0013

probability= 0.0013

e.

using z score formula

z =(X- ) / = 35 -40 / 5=-1

orchestra answered 1 year ago
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