Question

Study the binomial distribution table. Notice that the probability of success on a single trial p ranges from 0.01 to 0.95. Some binomial distribution tables stop at 0.50 because of the symmetry in the table. Let's look for that symmetry. Consider the section of the table for which n = 5. Look at the numbers in the columns headed by p = 0.30 and p = 0.70. Do you detect any similarities? Consider the following probabilities for a binomial experiment with five trials.

(a) Compare P(3 successes), where p = 0.30, with P(2 successes), where p = 0.70.

They are the same.P(3 successes), where p = 0.30, is smaller.    P(3 successes), where p = 0.30, is larger.

(b) Compare P(3 or more successes), where p = 0.30, with P(2 or fewer successes), where p = 0.70.

P(3 or more successes), where p = 0.30, is smaller.They are the same.    P(3 or more successes), where p = 0.30, is larger.

(c) Find the value of P(4 successes), where p = 0.30. (Round your answer to three decimal places.)
P(4 successes) =

For what value of r is P(r successes) the same using p = 0.70?
r =

(d) What column is symmetrical with the one headed by p = 0.20?

the column headed by p = 0.85the column headed by p = 0.50    the column headed by p = 0.40the column headed by p = 0.80the column headed by p = 0.70

Answer 1

Given:

Study the binomial distribution table.

Notice that the probability of success on a single trial p ranges from 0.01 to 0.95.

n = 5

p = 0.30 and p = 0.70

a)

P(3 successes)=0.1323 with P( 2 success) =0.1323

P(3 successes), where p = 0.30, is larger.

They are all same.

P(3 successes), where p = 0.30, is smaller.

b)

P( 3 or more successes )=0.163 with P( 2 or fewer successes) =0.163.

P(3 or more successes), where p = 0.30, is larger.

They are all same.

(3 or more successes), where p = 0.30, is smaller.

c) P(4 successes) = 0.028

So  r = 1

Therefore for r = 1 is P(r successes) the same using p = 0.70.

d) The column headed by p = 0.80 is symmetrical with the one headed by p = 0.20.

So C is the correct option.