Question

Using the normal approximation, find the approximate probability of at most 16 successes of 40. You may need to consult your z table or the shiny app

Answer 1

First, we will check conditions for normal distribtution

proportion = 16/40 = 0.4

sample size is n = 40

We have to conditions which must satisfy in order to use normal distribution

and

setting the values, we get

and

So, we can use normal distribution

Mean and standard deviation for the normal distribution are given as

Mean = np = 40*0.4 = 16

standard deviation =

Now, we have to find the probability of at most 16 successes means less than 16

using the formula

setting the given values x(bar) = 16, mu = 24 and sigma = 3.10

we get,

Using z distribution table (looking at -2.0 in the left most column and 0.58 in the top most row, selecting the intersection cell)

we get,

P(less than 16) = 0.0049