Sixty percent of the students applying to a university are accepted. Using the b

Question

Sixty percent of the students applying to a university are accepted. Using the binomial probability tables, what is the probability that among the next 12 applicants

a.

At least 6 will be accepted?

b.

Exactly 10 will be accepted?

c.

Exactly 5 will be rejected?

d.

Determine the expected number of acceptances.

e.

Compute the standard deviation.

a.

At least 6 will be accepted?

b.

Exactly 10 will be accepted?

c.

Exactly 5 will be rejected?

d.

Determine the expected number of acceptances.

e.

Compute the standard deviation.

Explanation / Answer

X ~ Binomial (n,p)

Where n = 12, p = 0.60

Biomial probability distribution is

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

a)

P( X >= 6) = 1 - P( X <= 5)

= 1 - 0.1582 (Probability calculated from cumulative binomial probability table)

= 0.8418

b)

P(X = 10) = 12C10 0.6010 0.402

= 0.0639

c)

Probability of rejection = 1 - 0.60 = 0.40

P( x = 5) = 12C5 0.405 0.607

= 0.2270

d)

E(X) = np

=12 * 0.60

= 7.2

e)

Standard deviation = Sqrt( np(1-p))

= Sqrt( 12 * 0.60 * 0.40)

= 1.6971

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