Question

The mean rate for satellite television from a sample of households was $49.00 with a standard deviation of $2.50. Assume that the distribution of satellite television rates is symmetric and bell-shaped.

a) Approximately 68% of households pay between

(b) Approximately what percentage of households pays more than $54.00?

(c) Approximately what percentage of households pays less than $41.5?

(d) If the rate of satellite television is $46.5, what is the corresponding z-score?

2)

Consider the following probability distribution for a discrete random variable X. Find the missing probability and answer the following questions.

X	-2	0	1	2	9
P(X)	0.1	?	0.2	0.3	0.1

(a) Find P(X>0)   

(b) The mean (expected value) of X is

(c) The standard deviation of X is closest to

Answer 1

1)

Here we have

a)

Since distribution is bell shaped so approximately 68% observations lie within one standard deviation of mean. That is required interval is:

b)

Since distribution is bell shaped so approximately 95% observations lie within two standard deviations of mean. That is required interval is:

That is approximately (95%/2) =47.5% data is between $49.00 and $54.00. The percentage of data above $54.00 is 50% - 47.5% = 2.5%.

c)

Since distribution is bell shaped so approximately 99.7% observations lie within three standard deviations of mean. That is required interval is:

That is approximately (99.7%/2) =49.85% data is between $41.85 and $49.00. The percentage of data below $41.85 is 50% - 49.85% = 0.15%.

(d)

The z-score for X = 46.5 is