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Basic Question 8 of 11
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?
B. approximately 1
C. approximately 0
A. P = 0.2500
B. approximately 1
C. approximately 0
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 (55-60)/1.633=-3.06185 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 insane..lol |
| 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: (55-60)/0.73=-6.84 |
| 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 |
I used your notes and passed ... highly recommended!
Lauren
Learning Outcome Statements
explain the central limit theorem and its importance for the distribution and standard error of the sample mean
CFA® 2024 Level I Curriculum, Volume 1, Module 7.