Use the normal approximation of the binomial probability

Question

Parallel treatments of a frequency distribution and a probably distribution.

Frequency Distribution

Complete the table below for the following data. (Recall that x is the midpoint of the interval.)

14, 7, 1, 11, 2, 3, 11, 6, 10, 13, 11, 11, 16, 12, 9, 11, 9, 10, 7, 12, 9, 6, 4, 5, 9, 16, 12, 12, 11, 10, 14, 9, 13, 10, 15, 11, 11, 1, 12, 12, 6, 7, 8, 2, 9, 12, 10, 15, 9, 3

Interval x Tally f xf
1-3 2 IIII I 6 12
4-6
7-9
10-12
13-15
16-18

Probability Distribution

A binomial distribution has n = 10 and p = .5. Complete the following table.

x  P(x) x P(x)
1  .001
2  .010
3  .044
4  .117
5
6
7
8
9
10

a. Find the mean (or expected value) for each distribution.

b. Find the standard deviation for each distribution.

c. Use the normal approximation of the binomial probability distribution to find the interval that contains 95.44% of that distribution.