Question

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

Stars   Frequency
1 2955
2 2537
3 3809
4 4537

5 10,637

a)Construct a discrete probability distribution for the random variable x. (round to 3 decimal places if needed)

b) Graph the discrete probability distribution. Choose the correct graph below.

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

Which of the following interpretations of the mean is​ correct?

A.

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

B.

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

C.

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

D.

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

​(d) Compute the standard deviation of the random variable x.

The standard deviation is ______ stars.

​(Round to one decimal place as​ needed.)

Answer 1

a) dividing each frequency value with total of 24475:

x	P(X=x)
1	0.121
2	0.104
3	0.156
4	0.185
5	0.435

b)

c)

x	P(X=x)	xP(x)	x2P(x)
1	0.121	0.12074	0.12074
2	0.104	0.20731	0.41463
3	0.156	0.46688	1.40065
4	0.185	0.74149	2.96597
5	0.435	2.17303	10.86517
total	1.00	3.7095	15.7672
	E(x) =μ=	ΣxP(x) =	3.7095
	E(x2) =	Σx2P(x) =	15.7672
	Var(x)=σ2 =	E(x2)-(E(x))2=	2.007067
	std deviation=	σ= √σ2 =	1.41671

from above mean  μ= 3.7095 (please try 3.7 if required to 1 decimals)

C.As the number of experiments​ increases, the mean of the observations will approach the mean of the random variable.

d)The standard deviation is =1.4