Suppose 55% of recent college graduates plan on pursuing a graduate degree. Nine

Question

Suppose 55% of recent college graduates plan on pursuing a graduate degree. Nineteen recent college graduates are randomly selected. (Use Excel) What is the probability that no more than four of the college graduates plan to pursue a graduate degree? (Round your intermediate calculations and final answer to 4 decimal places.) Probability What is the probability that exactly ten of the college graduates plan to pursue a graduate degree? (Round your intermediate calculations and final answer to 4 decimal places.) Probability What is the probability that at least eight but no more than twelve of the college graduates plan to pursue a graduate degree? (Round your intermediate calculations and final answer to 4 decimal places.) Probability

Explanation / Answer

Solution:-

Probability that recent college graduate will plane on pursuing graduate degree = 0.55

Number of students taken randomly = 19

a) The probability that no more than 4 of the college graduate plane to pursue graduate degree is P(x < 4) = 0.002756.

n = 19, x = 4, p = 0.55

By applying binomial distribution:-

P(x, n, p) = nCx*p x *(1 - p)(n - x)

P(x < 4) = 0.002756

b) The probability that exactly 10 of the college graduate plane to pursue graduate degree is P(x = 10) = 0.177.

n = 19, x = 10, p = 0.55

By applying binomial distribution:-

P(x, n, p) = nCx*p x *(1 - p)(n - x)

P(x = 10) = 0.177

c) The probability that atleast 8 but not more than 12 of the college graduate plane to pursue graduate degree is P(8 < x < 12) = 0.7456.

n = 19, p = 0.55

By applying binomial distribution:-

P(x, n, p) = nCx*p x *(1 - p)(n - x)

P(8 < x < 12) = P(x > 8) - P(x > 12)

P(8 < x < 12) = 0.91827 - 0.172659

P(8 < x < 12) = 0.7456

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