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.)

Answer 1

This can be solved using binomial distirbution

P(X=x) = ⁿC_x p^x ( 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