1. Suppose x has a binomial probability distribution with n = 200 and p = 0.60.
ID: 3362180 • Letter: 1
Question
1. Suppose x has a binomial probability distribution with n = 200 and p = 0.60. We want to determine if it is appropriate to use the normal approximation to the binomial. Which one of the following statements is true?
2. Find the probability of an observation lying more than z = 2.17 standard deviations above the mean.
3. Assume that 20% of all pigs die between birth and weaning. In a random sample of 300 births, let X be the number of pigs that die between birth and weaning. Using the normal approximation to the binomial, find the approximate probability that the number of pigs in the sample of 300 that die between birth and weaning is less than or equal to 50.
4. The mean length of time required to complete a 5K race was 20 minutes. The standard deviation of the times was 4 minutes. The racing times were approximately normally distributed. What is the probability that a randomly selected runner completed the race in less than 16 minutes?
It is appropriate to use the normal approximation to the binomial, because both 99.2154 and 140.7846 fall between 0 and n = 200.Explanation / Answer
1)
It is appropriate to use the normal approximation to the binomial, because n = 200, which is greater than 30.
2)
P(Z > 2.17) = 0.015
3)
mean = 300 * 20% = 60
standard deviation = sqrt(npq) = sqrt(300 * 20% * 80%)
= 6.928
P(X<=50) = P(Z < 50-60/6.928)
= P(Z < -1.4434)
= 0.0853
4)
P(X < 16) = P(Z < 16-20/4)
= P(Z < -1)
= 0.1587
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