Consider a binomial experiment with 15 trials and probability 0.35 of success on a single trial. (a) Use the binomial distribution to find the probability of exactly 10 successes (Round your answer to three decimal places.)
(b) Use the normal distribution to approximate the probability of exactly 10 successes. (Round your answer to three decimal places.) (
(c) Compare the results of parts (a) and (b).
A. These results are fairly different.
B. These results are almost exactly the same.

a

b

c

 Option A is correct

Step-by-step explanation:

From the question we are told that

     The sample size is   n =  15

     The  probability of success is  

     The number of success we are considering is  r = 10  

Now the probability of failure is mathematically evaluated as

substituting value

Now using  the binomial distribution  to find the probability of exactly 10 successes we have that

substituting values

Where   mean 15 combination 10  which is evaluated with a calculator to obtain  

So

Now using  the normal distribution to approximate the probability of exactly 10 successes, we have that

Applying continuity correction

substituting values

Standardizing  

The  where   is the mean which is mathematically represented as

substituting values

The standard deviation is evaluated as      

substituting values

Thus  

From the normal distribution table we obtain the as

And  the  

There value can also be obtained from a probability of z calculator at (Calculator dot net website)

So  

Looking at the calculated values for question a and b  we see that the values are fairly different.

she will travel a distance in the range of 3 - 11 miles