Question

A manager records the number of hours, X, each employee works on his or her shift and develops the probability distribution below. Fifty people work for the manager. How many people work 4 hours per shift?

Probability Distribution
Hours Worked: X
Probability: P(X)
3
0.1
4
?
5
0.14
6
0.3
7
0.36
8
0.06
0
1
2
4

Answer 1

2 people worked for 4 hours.

Explanation:

We are given X = No. of hours worked

And we are also given that No. of people work for the manager = 50

X = 3, 4 , 5 , 6 , 7, 8

P(X) = 0.1 , ? , 0.14 , 0.3 , 0.36 , 0.06

Since sum of all the probabilities =1

So,

0.1 + ? + 0.14 + 0.3 + 0.36 + 0.06 =1

0.96+? =1

? = 1 - 0.96

? = 0.04

So, probability of no. of people worked for 4 hours = 0.04

P(4)=0.04

So, no. of people worked for 4 hours =50*P(X)

=50*0.04

=2

Hence 2 people worked for 4 hours.

Answer 2

c. 2

Explanation:

Given : X = No. of hours worked

No. of people work for the manager = 50

X = 3, 4 , 5 , 6 , 7, 8

P(X) = 0.1 , ? , 0.14 , 0.3 , 0.36 , 0.06

To Find : No. of people work for four hours

Solution : First understand the fact that sum of all probabilities is equal to 1

So, sum of all values of P(X) = 1

⇒
`0.1+?+0.14+0.3+0.36+0.06 = 1`

⇒
`0.96+? = 1`

⇒
`?= 1-0.96`

⇒
`? = 0.04`

So, the probability of no. of people worked for 4 hours is 0.04.

⇒P(4)=0.04

Thus , To calculate no. of people work for four hours :

`0.04* 50`

⇒ 2 no. of people work for four hours per shift .