Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 121 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. Probability that fewer than 33 voted
The probability that fewer than 33 of 121 eligible voters voted
is .
(Round to four decimal places as needed.)
Answer)
N = 121
P = 0.22
First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not
N*p = 26.62
N*(1-p) = 94.38
Both the conditions are met so we can use standard normal z table to estimate the probability
Z = ( x - mean)/s.d
Mean = n*p = 26.62
S.d = √{(n*p*(1-p)} = 4.55670933898
We need to find
P(x<33)
By continuity correction
P(x<32.5)
Z = (32.5 - 26.62)/4.55670933898
Z = 1.29
From z table, P(z<1.29) = 0.9015
Required probability is 0.9015
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