Yes, the mean is 26.4 and the standard deviation is 3
We are given;
n = 40, p = 66% = 0.66, and q = 1 – 0.66 = 0.34
If np ≥ 5 and np ≥ 5, then the binomial random variable, x is approximately normally distributed, then;
Mean; µ = np
Standard deviation; σ = √npq
where;
n is the sample size.
p is the population proportion.
q = 1 – p.
Calculating np and nq gives;
np = (40)(0.66) = 26.4
nq = (40)(0.34) = 13.6
Both np and nq are greater than 5, the normal distribution can be used to approximate the binomial distribution.
Thus, µ = np
µ = 40(0.66) = 26.4
Standard deviation;
σ = √(40 * 0.66 * 0.34)
σ = 3
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