Question

While being interviewed about the status of education, a politician states that at least
20% of all new teachers leave the profession within the first three years. If 216
teachers hired three years ago are selected

While being interviewed about the status of education, a politician states that at least
20% of all new teachers leave the profession within the first three years. If 216
teachers hired three years ago are selected at random, find the probability that 33 or
fewer teachers were no longer teaching.

Answer 1

Solution:

Given that,

p = 20% = 0.20

1 - p = 1 - 0.20 = 0.80

n = 216

Here, BIN (216 , 0.20)

then,

n*p = 216 * 0.20 = 43.2

n(1- p) = 216 * 0.80 = 172.8

Since both are greater than 5 , we can use normal approximation to binomial.

According to normal approximation binomial,

X Normal

Mean = = n*p = 43.2

Standard deviation = =n*p*(1-p) = 34.56 = 5.87877538268

Now ,

P(33 or
fewer teachers were no longer teaching.)

= P(X   33)

= P[(X - )/     (33 - )/]

= P[Z   (33 - 43.2)/5.87877538268]

= P[Z -1.735]

= 0.0414 ... ( use z table)

Required probability = 0.0414