Answer and Explanation:
Given : The random variable x has the following probability distribution.
To find :
a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.
b. Calculate the expected value of x.
c. Calculate the variance of x.
d. Calculate the standard deviation of x.
Solution :
First we create the table as per requirements,
x P(x) xP(x) x² x²P(x)
0 0.25 0 0 0
1 0.20 0.20 1 0.20
2 0.15 0.3 4 0.6
3 0.30 0.9 9 2.7
4 0.10 0.4 16 1.6
∑P(x)=1 ∑xP(x)=1.8 ∑x²P(x)=5.1
a) To determine that table shows a probability distribution we add up all five probabilities if the sum is 1 then it is a valid distribution.


Yes it is a probability distribution.
b) The expected value of x is defined as

c) The variance of x is defined as

d) The standard deviation of x is defined as



Distance Rate times Time
320= R 5.25
R= 60.9
R= 61 mph
Solve system of inequalities graphically
Answer:
Mean of sampling distribution = 25 inches
Standard deviation of sampling distribution = 4 inches
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 25 inches
Standard Deviation, σ = 12 inches
Sample size, n = 9
We are given that the distribution of length of the widgets is a bell shaped distribution that is a normal distribution.
a) Mean of the sampling distribution
The best approximator for the mean of the sampling distribution is the population mean itself.
Thus, we can write:

b) Standard deviation of the sampling distribution

6 divided by 10 would be 60 percent and .60 as a decimal