Question

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. It is estimated that 3.6% of the general population will live past their 90th birthday. In a graduating class of 761 high school seniors, find the following probabilities. (Round your answers to four decimal places.) (a) 15 or more will live beyond their 90th birthday Incorrect: Your answer is incorrect. (b) 30 or more will live beyond their 90th birthday (c) between 25 and 35 will live beyond their 90th birthday (d) more than 40 will live beyond their 90th birthday.

Answer 1

Here n=761 and p=0.036

So np>5 and nq>5

Hence we can use the normal approximation

Now we can see that distribution here is binomial

So mean value is and standard deviation is

a. Here we need to find

As normal distribution can be used we will convert x to z

b.

c.

d.

So answer here is 0.0071