Question

QUESTION PART A: A population of values has a normal distribution with μ=156μ=156 and σ=43.2σ=43.2. You intend to draw a random sample of size n=135n=135.

Find the probability that a single randomly selected value is greater than 146.7.
P(X > 146.7) =

Find the probability that a sample of size n=135n=135 is randomly selected with a mean greater than 146.7.
P(M > 146.7) =

PART B: A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 163.5-cm and a standard deviation of 1.2-cm. For shipment, 13 steel rods are bundled together.

Find the probability that the mean length of a randomly selected bundle of steel rods is greater than 163.8-cm.
P(¯xx¯ > 163.8-cm) =

Answer 1

Given That Il = 156 ; 0:43.2 05135 Pl single randanty selected valie >1464) nel P(X>146.7) = 1-P{ x < 146.7] =1-PZ 2 146.7-1567 43.2 & 146.17 = 1-Plz 1 -p22 -0.215] = 1-0-4149 - 0.5851 2 146.7-156 P(x> 146-7) - 0.5851 n=185 PM > 1467) p(M> 146-7) - 1-PCM< 146.7) = 1-P122 123 124 El-P[z 2-2.5) from z table 100062 0.9938 P(MS 1467) = 0.9938

B) Man = 1635 Standard deviation in =13 Plz 1638) - 1-P[< <1638] ala pſz < 163.8 - 1635 7 12/03 =-P[ze 2.982] =-P[720.90] from 1 table = 1-0.8186 ; 0.1814 P(x >63.8 = 0.181H