Solution Found!
Answer: In Exercise, determine whether you can use a
Chapter , Problem 6CT(choose chapter or problem)
Problem 6CT
In Exercise, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities.
A survey of U.S. adults ages 25 and older found that 86% have a high school diploma. You randomly select 30 U.S. adults ages 25 and older. Find the probability that the number who have a high school diploma is (a) exactly 25, (b) more than 25, and (c) less than 25, and (d) identify any unusual events. Explain.
Questions & Answers
QUESTION:
Problem 6CT
In Exercise, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities.
A survey of U.S. adults ages 25 and older found that 86% have a high school diploma. You randomly select 30 U.S. adults ages 25 and older. Find the probability that the number who have a high school diploma is (a) exactly 25, (b) more than 25, and (c) less than 25, and (d) identify any unusual events. Explain.
ANSWER:
Solution 6CT
Step1 of 5:
From the given problem we have
Here our goal is:
a). We need to find the probability of exactly 25 have a high school diploma.
b). We need to find the probability of more than 25 have a high school diploma.
c). We need to find the probability of less than 25 have a high school diploma.
d). We need to identify any unusual events in above part (a), part(b), and part (c).
Introduction:
Yes we can use a normal distribution to approximate the binomial distribution. And the procedure is given below:
1).Suppose ‘x’ follows binomial distribution with parameters ‘n and p’. Then, The mean of a Binomial distribution is:
The standard deviation of binomial distribution is:
Where,
2).Suppose ‘x’ follows Normal distribution with parameters ‘’. Then, The mean of a Normal distribution is:
The standard deviation of Normal distribution is:
Now, a normal distribution to approximate the binomial distribution is:
Therefore,