Mathematics - Finite Mathematics

Hi, I need help with this assignment. I will be using this to check my work, so it very important that all work is shown so that I have a clear idea of how each problem is done. I am only interested in the completed assignment- not just some of it. Thank you very much for your help! :) (Please see the attached file)

Instructions
Answer all the problems in the template below. Be sure to show and input all work into the correct cells. Graphs and work done in Excel can be copied and pasted into the cells. Thanks!

Page # Prob. # Problem and Solution:

446 2 How many variations in the first-, second-, and third-place finishes are possible in a 100-yd dash with 6 runners?

447 20 Suppose a family plans 6 children, and the probability that a particular child is a girl is ½. Find the probabilities that the 6-child family has at least 4 girls.

22 Suppose 2 cards are drawn without replacement from an ordinary deck of 52. Find the probability that both cards are red.

30 Give the probability that corresponds to the shaded region of the histogram.

32 You pay $6 to play in a game where you will roll a die with payoffs as follows: $8 for a 6, $7 for a 5, and $4 for any other results. What are you expected winnings? Is the game fair?

40 A certain machine that is used to manufacture screws produces a defect rate of 0.01. A random sample of 20 screws is selected. Find the probabilities that the sample contains exactly 3 defective screws.

500 4 The number of units carried in one semester by students in a business mathematics class was as follows. Use intervals 9-10, 11-12, 13-14, 15-16 to do the following:(a) write a frequency distribution; (b) draw a histogram; (c) draw a frequency polygon
10 9 16 12 13 15 13 16 15 11 13
12 12 15 12 14 10 12 14 15 15 13

(a) write a frequency distribution

(b) draw a histogram

(c) draw a frequency polygon

6 Find the mean for the following.
105, 108, 110, 115, 106, 110, 104, 113, 117

8 Find the mean for the following.
Interval Frequency
40-44 2
45-49 5
50-54 7
55-59 10
60-64 4
65-69 1

501 10 Find the median and the mode (or modes) for the following:
32, 35, 36, 44, 46, 46, 59

16 Find the range and the standard deviation for the following:
14, 17, 18, 19, 32

22 Find the area under the standard normal curve between z = 0 and z = 1.27.

26 Find a z-score such that 8% of the area under the curve is to the right of z.

502 34 The probability that a small business will go bankrupt in its first year is 0.21. For 50 such small business, find the following probabilities by using either the binomial probability formula or by using the normal approximation.

a. Exactly 8 go bankrupt.

b. No more than 2 go bankrupt.