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24.07.2019 •
Mathematics
Amarket research firm conducts telephone surveys with a 41% historical response rate. a. what is the probability that in a new sample of 400 telephone numbers, at least 135 individuals will cooperate and respond to the questions? in other words, what is the probability that the sample proportion will be at least 135/400 = 0.3375?
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Ответ:
probability is 0.778
Step-by-step explanation:
Given data in question
success of probability (p) = 41% = 0.41
no of sample (n) = 400
individual = 150
to find out
probability that the sample proportion will be at least 135/400
solution
first we calculate the mean i.e
mean = p × n
mean = 400 × 0.41
mean = 164
now we calculate standard deviation =![\sqrt{400(0.41) 0.59}](/tpl/images/0128/0279/22778.png)
standard deviation = 9.83666
we know P(X ≥ 135) = P(Z ≥ (150 - 164)/9.83666)
P(X ≥ 135) = P(Z ≥ (-1.42324)
from table 1 find corresponding probability
P(X ≥ 135) = 1 - P(Z ≥ (-1.42324)
= 1 - 0.9222 = 0.778
probability is 0.778
Ответ: