Maths Question

Scarbo

2012-11-04 12:29 pm

1. a) 3% of the components producedon a certain assembly machine are defective. Find the probability that in asample of 50 components:(i) 0 will be defective, (ii) 1 will be defective,(iii) 1 or less will be defective, (iv) 2 or more will be defective b) In a shopping complex, 1000electric lamps are installed. These lamps have a mean burning life of 1100 hourswith a standard deviation of 250 hours.(i) How many lamps are likely tofail during the first 800 burning hours ?(ii) How many lamps are likelyto fail between 900 and 1400 burning hours ? (iii)Howmany lamps are likely to work after 1600 hours ?
Thanks!

更新1:

To myisland8132: How can I get the answer from Step 2 to Step 3 (ii) P(900 <= T <= 1400) = P(-0.8 <= Z <= 1.2) <-- Step 2 = 0.6731 <-- Step 3 So, around 673 lamps will be failed

回答 (1)

myisland8132

2012-11-04 7:03 pm

✔ 最佳答案

1(a)(i) Let X be the no. of defectives

P(X = 0) = (0.97)^50 = 0.218065

(ii) P(X =1) = 50 (0.03)(0.97)^49 = 0.3372

(iii) P(X <= 1) = 0.218065 + 0.3372 = 0.555265

(iv) P(X >= 2) = 1 - 0.555265 = 0.444735

(b) Let T be the burning life

P(T <= 800)

= P(Z <= (800 - 1100)/250)

= P(Z <= -1.2)

= 0.1151

So, around 115 lamps will be failed

(ii) P(900 <= T <= 1400)

= P(-0.8 <= Z <= 1.2)

= 0.6731

So, around 673 lamps will be failed

(ii) P(T >= 1600)

= P(Z >= 2)

= 0.02275

So, around 22 or 23 lamps will be work after 1600 hours

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