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Solution: In Exercise, determine whether you can use a
Chapter , Problem 69E(choose chapter or problem)
Problem 69E
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 found that 52% of U.S. teens ages 16 to 18 have a savings account. You randomly select 45 U.S. teens ages 16 to 18 and ask them whether they have a savings account. Find the probability that the number who have a savings account is (a) at most 15, (b) exactly 25, and (c) greater than 30, and (d) identify any unusual events. Explain.
Questions & Answers
QUESTION:
Problem 69E
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 found that 52% of U.S. teens ages 16 to 18 have a savings account. You randomly select 45 U.S. teens ages 16 to 18 and ask them whether they have a savings account. Find the probability that the number who have a savings account is (a) at most 15, (b) exactly 25, and (c) greater than 30, and (d) identify any unusual events. Explain.
ANSWER:
Solution:
Step 1 of 5:
Given, in a survey 52% of U.S. teens ages 16 to 18 have a savings account.
If we randomly select 45 U.S. teens ages 16 to 18 and ask them whether they have a savings account.
If a Binomial distribution is approximated by a Normal distribution if np and nq are greater than or equal to 5.
n = 45 and p = 0.52.
np = 45(0.52)
= 23.4 and
nq = 45(1 - 0.52)
= 21.6.
Both np and nq are greater than 5.