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.
106 115 115 111 112 104 87 119 135 104
128 124 109 124 93 119 113 133 117 95
102 103 109 137 126 120 116 103 121 111
116 106 99 113 120 109 98 102 105 90
121 103 111 110 113 114 122 103 102 72
106 114 108 102 89 112 100 123 95 101
111 119 100 118 117 104 106 93 116
For the Full description of the questions please see the attached question file.
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
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
Probability: NBA (National Basketball Association) application
Probability questions on NBA.
ONLY DO PROBLEM 1 and 2 from the four questions in the document.
Problem 1 ? Consider the NBA Data Set Given:
A. What proportion of these players are less than 74 inches tall?
B. Suppose a random sample of 25 of these players is taken and x is the number of players in the sample who are less than 74 inches tall. Find P(x=0), P(x=1), P(x=2), P(x=3), P(x=4), P(x=5).
C. Note that x in part b has a binomial distribution with lambda=np. Use the Poisson probabilities table to approximate P(x=0), P(x=1), P(x=2), P(x=3), P(x=4), P(x=5).
D. Are the probability distributions of parts b and c consistent or is the Poisson approximation inaccurate. Explain.
Problem 2 ? Consider the Data on Heights of NBA Players in the Data Set Given:
A. Use Excel to obtain a histogram. Do these heights appear to be symmetrically distributed? If not, which direction do they seem to be skewed?
B. Compute mu and sigma.
C. What percentage of these heights lie in the interval mu - sigma to mu + sigma? What about in the interval mu - 2 sigma to mu + 2 sigma? In the interval mu - 3 sigma to mu + 3 sigma?
D. How do the percentages in part c compare to the corresponding percentages for a normal distribution (68%, 95%, and 99.7% respectively)?