Use following information to answer questions10 11 12 The ti

Use following information to answer questions10, 11, 12

The time spent (in minutes) in reading newspaper for an adult per day can be approxiimated by a normal distribution with mean = 15 minutes and stdv = 3 minutes.

10) Find the probability that the reading time per day for a randomly selected adult ismore than 18 minutes

a) 0.1587   b) 0.8413     c) 0.6826    d) 0.6587     e) 1.0000

11) If 200 adults are randomly selected, approximately how many of them will spend in

reading newspaper per day between 12 minutes and 19.5 minutes.

a) 32      b) 168   c) 187      d) 136     e) 155

12) What is the shortest time spent in reading newspaper for an adult per day that would still place him in the top 10% ?

a) 15.30 b) 15.90   c) 18.84   d) 11.16    e) 15.10

Solution

i) z = (X-Mean)/SD
z = (18-15)/3 = + 1
Required Probability = P(X>18)
= P(z>1)
= >1-P(z<1)=>1-..8413=0.1587
CHOICE (a) is the answer

ii) z1 = (12-15) / 3 = - 1
z2 = (19.5-15)/3 = + 1.5
Expected number = P(12 < X < 19.5) * 200
= P(-1 < z < 1.5) * 200
= [P(z < 1.5) - P(z < - 1)] * 200
= [0.9332 - 0.1587] * 200
= 0.7745 * 200
= 154.9 or 155
CHOICE (e) is the answer

iii) Top 10% is represented by 0.1000 area under the standard normal curve in its extreme right tail
The z value which separates the top 0.1000 area from the rest is + 1.28
1.28 = (X-15)/3
X = 15 + (1.28*3) = 18.84