3 The random variable X is binomially distributed with n35 a

[3] The random variable X is binomially distributed, with n=35 and p=0.4. I want to calculate the probability (P X leq 12); do not calculate the probability that is not question. Can I do so, calculate the probability, using a normal approximation? A yes or no answer alone will not receive any credit. You must indicate/show why your answer is correct.

Solution

Answer: yes, we can use normal approximation

n=35

p=0.4

normal distribution as an approximation to the binomial when np > 5 and n(1 - p) > 5

in this case

np= 35*0.4 =14

n(1-p)=35*(1-0.4) =21

both np and n(1-p) > 5

we can use normal approximation