Suppose 44% of recent college graduates plan on pursuing a graduate degree. Twen

Question

Suppose 44% of recent college graduates plan on pursuing a graduate degree. Twenty six recent college graduates are randomly selected.

a. What is the probability that no more than seven of the college graduates plan to pursue a graduate degree? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

b. What is the probability that exactly thirteen of the college graduates plan to pursue a graduate degree? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

c. What is the probability that at least ten but no more than fourteen of the college graduates plan to pursue a graduate degree? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

Explanation / Answer

This can be solved using binomial distirbution

P(X=x) = nCx px ( 1- p )n-x

where, n = Number of trials

p = Probability of success

In our case , n = 26 and p = 44% = 0.44

a. Probability that no more than seven of the college graduates plan to pursue a graduate degree=

= P( X < = 7 )

= P(X=0) + P(X=1) + P(X=2 ) + .................... + P(X = 7)

= 26C0 0.440 ( 1- 0.44 )26-0 + 26C1 0.441 ( 1- 0.44 )26-1 + ............+ 26C7 0.447 ( 1- 0.44 )26-7

= 0.0575

b. Probability that exactly thirteen of the college graduates plan to pursue a graduate degree =

= P(X=13)

= 26C13 0.4413 ( 1- 0.44 )26-13

= 0.1283

c. Probability that at least ten but no more than fourteen of the college graduates plan to pursue a graduate degree

= P(X = 10) + P(X=11) + ........................ + P(X=14)

=  26C10 0.4410 ( 1- 0.44 )26-10 + 26C11 0.4411 ( 1- 0.44 )26-11 + ............+ 26C14 0.4414 ( 1- 0.44 )26-14

= 0.6632

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