Question

In an experiment of toss a fair coin 36 times. We want to use the normal distribution to approximate this binomial probability, what is the mean  and the standard deviation  to be used in normal distribution? ( Round to 1 decimal place) A) = 25,  = 3.8 B)  = 6,  = 3 C)  = 18,  = 3 D)  = 15,  = 3.6

Answer 1

Given that,

Sample size (n) = 36

In fair coin P(Head) = P(Tail) = 0.5

That is p = 0.5 and (1 - p) = 1 - 0.5 = 0.5

Mean and standard deviation in Binomial distribution is,

Mean $(\mu)$ = $np = 36*0.5=18$

Standard deviation $(\sigma)$ = $\sqrt{np(1-p)} = \sqrt{36*0.5*0.5}= \sqrt{9} = 3$

Hence,

Answer: C) $\mu = 18$ , $\sigma = 3$