Question

A study on recycling shows that in a certain city, each household accumulates an average of 14 pounds of newspapers each month to be recycled. The standard deviation is 2 pounds. If a household is selected at random, find the probability it will accumulate the following: a. Between 13 and 17 pounds of newspapers for one month b. More than 16.2 pounds of newspapers for one month. 4. An exclusive college desires to accept only the top 10% of all graduating seniors on the basis of the results of a national placement test. This test has a mean of 500 and a standard deviation of 100. Find the cutoff score for the exam.

Answer 1

a) P(13 < X < 17)

= P((13 - $\mu$ )/ $\sigma$ < (X - $\mu$ )/ $\sigma$ < (17 - $\mu$ )/ $\sigma$ )

= P((13 - 14)/2 < Z < (17 - 14)/2)

= P(-0.5 < Z < 1.5)

= P(Z < 1.5) - P(Z < -0.5)

= 0.9332 - 0.3085

= 0.6247

b) P(X > 16.2)

= P((X - $\mu$ )/ $\sigma$ > (16.2 - $\mu$ )/ $\sigma$ )

= P(Z > (16.2 - 14)/2)

= P(Z > 1.1)

= 1 - P(Z < 1.1)

= 1 - 0.8643

= 0.1357

4) P(X > x) = 0.1

or, P((X - $\mu$ )/ $\sigma$ > (x - $\mu$ )/ $\sigma$ ) = 0.1

or, P(Z > (x - 14)/2) = 0.1

or, P(Z < z) = 0.9

or, z = 1.28

or, (x - 500)/100 = 1.28

or, x = 1.28 * 100 + 500

or, x = 628