CFA Practice Question

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CFA Practice Question

A manufacturer of light bulbs claims that the distribution of the light bulb life span has a mean of 60 hours and a standard deviation of 4 hours. The competition decides to check this claim by purchasing 30 light bulbs and testing them to determine the life span of the light bulbs. What is the probability that the competition will find that the sample has a mean of 55 hours or fewer?

A. P = 0.2500
B. approximately 1
C. approximately 0
Correct Answer: C

User Contributed Comments 23

User Comment
Khadria Range = Mean +- Standard deviation = 56 hrs to 64 hrs

Hence below P(<55 hrs) ~ 0
Rotigga S=(4^2/60)^0.5=1.633
Z(-3.06185) ~ 0
epizi I think the answer is simple from a glance.Normal distribution, thesample mean x-bar=population mean.
So P(X-bar<55)=0
rtvlad In Rotigga's comment, why in calculating S=(a^2/60)^0.5 the N=60 is used. The problem gives 30, am I wrong?
StanleyMo rtv,
Yes N=30 should be used. You will still get the same answer.
steved333 Not sure where you guys are getting (sig^2/N)^.5, considering the notes and previous questions solve for std error as sigma/sqrtN...
JimM SD of sample is 4 / 30^0.5 = 0.7303
z-score = 5 / .7303 = 6.8+
55 hours or less is over 6 SDs away, therefore essentially 0% chance.
wundac Thanks JimM for clarifying this. I'm not sure where all these other answers were coming from.
Shalva 2wundac:

the other answers were coming from more or less the same material, but JimM got it best
thekid Thanks JimM

I thought it was me going
jpducros JimM, we'll call you Big Jim now...
gmilchev Thanks Jim.
poomie83 Jim for president!
EminYus i read all those comments until I got to Jim's who made the most sense
acemaj Jim, you are the man, bro!
Kaloyan Jim, Jim, Jim! :-)
Kaloyan Jim and All,

Not that it matters, but the z-score is negative:

Bududeen kaloyan for president then
sgossett86 JIM Yeah dude. all these other answers... I thought i was going crazy too. I'm trying to stick to the script here as much as possible.
ldfrench Hell yeah, Jim! You are fuckin seck
ascruggs92 Rottiga, while you got the answer right, the work you show in your comment is so horrendously wrong that you should delete your comment so as not to confuse other people
Marinov What I don't get here is that we are looking for the probability to the left of
-N and in the table we need to take N(x) rather than 1-N(x). Normally, by looking at the table for -2,5 the answer should be 1 - 0.
ashish100 Jim is our savior!! Thank you Jiiimmmyyyy
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