Answer
Yes, we can use the normal distribution to approximate the binomial distribution. Hence,
Mean = 32.5 and standard deviation $\approx$ 3.373.
Work Step by Step
n = 50, p = 0.65, q = 0.35
np = 50 x 0.65 = 32.5
nq = 50 x 0.35 = 17.5
Remember: If np $\geq$ 5 and nq $\geq$ 5, we can use the normal distribution to approximate the binomial.
Since np $\geq$ 5 and nq $\geq$ 5, we can use the normal distribution to approximate the binomial.
Hence,
Mean = np = 32.5
Standard Deviation = $\sqrt{npq}$ = $\sqrt{50\times0.65\times0.35}$ $\approx$ 3.373
