Question

Suppose the following data represent the rating (on a scale from 1 to 5) for a certain smart phone game, with 1 representing a poor rating. Complete parts (a) below

Stars --- Frequency

1 =. 2524

2 =. 2947

3 =. 3955

4 =. 3938

5 = 10,170

(a) Construct a discrete probability distribution for the random variable X [ hint: p(xi) =fi-n]

Stars (x)- P(x)

1    - ?

2        -       ?

3        -       ?

4        -       ?

5        -       ?

(Round to three decimal places as needed)

(b) Graph the discrete probability distribution.

(c) Compute and interpret the mean of the random variable X.

The mean is ? Stars

(Round to one decimal place as needed

which of the following interpretations of the mean is correct?

a. The observed value of the random variable will be less than the mean of the random variable in most experiments

b. As the number of experiments n decreases, the mean of the observations will approach the mean of the random variable.

c. As the number of experiments n decreases, the mean of the observations will approach the mean of the random variable.

d. The observed value of the random variable will be equal to the mean of the random variable in most experiments.

(d) Compute the standard deviation of the random variable X.

The standard deviation is ? Stars

(Round to one decimal place s needed)

Answer 1

a)

x	P(x)
1	0.107
2	0.125
3	0.168
4	0.167
5	0.432

b)

c)

x	f(x)	xP(x)	x2P(x)
1	0.107	0.1072	0.1072
2	0.125	0.2504	0.5009
3	0.168	0.5042	1.5125
4	0.167	0.6693	2.6773
5	0.432	2.1607	10.8035
	total	3.6919	15.6015
	E(x) =μ=	ΣxP(x) =	3.6919
	E(x2) =	Σx2P(x) =	15.6015
	Var(x)=σ2 =	E(x2)-(E(x))2=	1.9714
	std deviation=	σ= √σ2 =	1.4041

The mean is 3.70

As the number of experiments n increases, the mean of the observations will approach the mean of the random variable

d)

The standard deviation is =1.4