Question

The table below is a discrete probability distribution of study hours for mathematics in a given week.

  

Hours (x)	1	2	3	4	5
P(x)	0.16	0.22	?	0.20	0.14

1. Find the probability of x=3.
2. Find the mean and the standard deviation of this probability distribution.
3. Find the probability that x is at most 4 hours.

Answer 1

1. The table below is a discrete probability distribution of study hours for mathematics in a given week.

  

Hours (x)	1	2	3	4	5
P(x)	0.16	0.22	?	0.20	0.14

Find the probability of x=3.

Probabilities have to sum up to one when you are dealing with mutually exclusive events that encompass all possible outcomes.Simply, the sum of the probabilities in a probability distribution is always 1.

P(x=1) + P(x=2) + P(x=3) + P(x=4) + P(x=5) = 1

0.16 + 0.22 + P(x=3)+ 0.20 + 0.14 = 1

P(x=3) = 0.28

Find the mean and the standard deviation of this probability distribution.

Mean or Expected Value: μ

When we know the probability p of every value x we can calculate the Expected Value (Mean) of X:

μ = Σxp

Note: Σ is Sigma Notation, and means to sum up.

To calculate the Expected Value:

• multiply each value by its probability
• sum them up

Standard Deviation: σ

The Standard Deviation is the square root of the Variance:

σ = √Var(X)

Var(X) = Σx²p − μ²

σ =√1.6164= 1.2714

Find the probability that x is at most 4 hours.

P(x) = P(x=1) + P(x=2) + P(x=3) + P(x=4) = 0.16 + 0.22 + 0.28 + 0.20 = 0.86