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Tink2334
23.07.2019 •
Mathematics
Given a normal random variable x with mean 20 and variance 9, and a random sample of size n taken from the distribution, what sample size n is necessary in order that p(19.9 ≤ x ≤ 20.1) = 0.95?
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Ответ:
It can be noted that: error = 20.1-20=20-19.9 = 0.1
Therefore,
0.1= Z*sd/sqrt (n) => n = {Z*sd/0.1}^2
At 95% confidence interval, Z = 1.96, sd = sqrt (variance) = sqrt (9) = 3
Then,
Necessary sample size is,
n = {1.96*3/0.1}^2 = 3457.44 =3,458
Ответ:
45%
Step-by-step explanation: