Frequency Distribution - Histogram, Poisson Approximation to

Question (1):
The data in the table below relate to cadence. Form a frequency distribution using the classes 70 - 79.9 , 80 - 89.9 ...., 130 - 139.9

Display the information as a histogram. Use your frequency table to calculate an estimate of the mean and sample standard deviation if this data. Determine a 95% confidence interval for the population mean, clearly stating any assumptions you have made.

For the Full description of the questions please see the attached question file.

Question (2)
The probability that a patient will have an allergic reaction to a particular pain killing drug is 0.01.

(i)If a group of 15 patients are given this drug, what is the probability that one person has an allergic reaction ?
(ii)Using the Poisson approximation to the binomial, what is the probability that no one in a group of 120 patients has an allergic reaction ?

Class Interval Frequency
70 - 80 1
............ ........
......... ...

Solution Summary

The problems given in the attached file are explained in the attached solution file with each step and detailed explanation. One problem explains how to form a Frequency Distribution from raw data, how to draw a Histogram for the prepared distribution, How to find the Mean and Standard Deviation, How to find the 95% confidence interval for the population mean.
The second problem is related to Poisson Distribution to Binomial. Each and every step in the solution is very clear and students can work out other similar problems using this solution.
The problem is to find the probability of one person has an allergic reaction out of 15 and
probability that no one in a group of 120 patients has an allergic reaction

Please use words to describe the solution, not just symbols. (basically, explain what is going on in addition to an answer) Use a math symbol editor where appropriate.
Problem 1:
Write a program to compute binomial probabilities and compare the results with the Poissonapproximation for the following cases:
a) P(X = 2)

1. The following are marks obtained by a group of 40 students on an English examination:
42 88 37 75 98 93 73 62
96 80 52 76 66 54 73 69
83 62 53 79 69 56 81 75
52 65 49 80 67 59 88 80
44 71 7

I am trying to figure out how to enter data to create a histogram based on the following info. I want to create the histogram based on the cumulative frequencydistribution. Any help is appreciated. Thanks.
Pennies by Year:
Year # of Coins
1967 3
1968 2
1969 2
1970 1
1971 1
1972 2
1974 1
1975 1
1976 1
1977 3
19

The number of incoming phone calls at a company switchboard during 1-minute intervals is believed to have a Poissondistribution. Use a=.10 and the following data to test the assumption that the incoming phone calls follow a Poissondistribution.
# of Incoming Phone Calls During a 1-min Interval Observed Frequency
0

1. Place the following scores in a frequencydistribution table. Include columns for proportion (p) and percentage (%) in your table. The scores are: 4, 6, 2, 9, 8, 8, 5, 7, 7, 3, 6, 6, 7, 4, 5, 8, 6, 5
2. Under what circumstances should you use a grouped frequencydistribution instead of a regular frequencydistribution?

Radiation: The atoms of a radioactive element are randomly disintegrating and
emitting alpha particles. The number of alpha particles emitted per second from
these atoms during a 30 second period is recorded as follows.
9.38
8.08
8.36
10.44
9.44
8.05
17.78
7.56
14.17
6.73
9.81
4.79
11.98
9.48
6.32
14.

Let X have a Poissondistribution with a mean of 4. Find
a) P(23)
c) P(X<3)
Let X have a Poissondistribution with a variance of 4. Find P(X=2)
Customers arrive at a travel agency at a mean rate of 11 per hour. Assuming that the number of arrivals per hour has a Poissondistribution, give the probability th

Chest circumference for 5732 militiamen, Data was collected by an army contractor who was responsible for providing clothing for militia. A frequencydistribution for the chest circumferences in inches is given
Chest size (in.) Frequency
33 3
34 19
35 81
36 189
37 409
38 753
39 1062
40 1082
41 935
42 646
43 313
44 1

Please help with the following problems. See attached file for proper table format.
Accounting Horizons published a 1998 study in which corporate executives reported the number of times each year they held audit committee meetings with the chief internal auditor of the corporation. The raw data are shown below:
0 0 0 0 0