Answer
Answer: Yes, we can use the normal distribution to approximate the binomial. Hence, Mean = 22 and Standard Deviation $\approx $3.146.
Work Step by Step
n = 40, p = 0.55, q = 0.45
np = 40 x 0.55 = 22
nq = 40 x 0.45 = 18
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 = 22
Standard Deviation = $\sqrt{npq}$ = $\sqrt {40\times 0.55\times0.45}$ $\approx$ 3.146
