4. A cigarette manufacturing company claims that the mean nicotine content of it

Question

4. A cigarette manufacturing company claims that the mean nicotine content of its king size cigarettes is p = 2 mg, and that the nicotine content standard deviation is o= 0.3 mg. Assuming the claim to be valid, answer the following questions. (a) What is the probability that the average nicotine content of 125 of these king sized cigarettes will exceed 2.02 mg.? What needs to be true about these 125 cigarettes to answer this question? Exactly 25% of the time, the total amount of nicotine in 15 randomly sampled packs of these king sized cigarettes will not exceed how many mg.? Note that there are 20 cigarettes per pack. What is the probability that a random sample of 4 of these king sized cigarettes will contain a total of more than 7 mg of nicotine ? (c) What I

Explanation / Answer

a)

we are assuming that sample has taken randomely and are independent.

threfore probability that average exceed 2.02 gm

b) total number of cigrettes =15/20 =300

hence total average nicotine =2*300 =600 mg

std deviation =0.3*(300)1/2 =5.20

for 25 percentile ; z score =-0.6745

corresponding nicotine content =mean+z*std deviation =600-0.6745*5.20=596.50 mg

c)

otal average nicotine =2*4 =8 mg

std deviation =0.3*(4)1/2 =0.6

hence probability that 4 will contain more than 7 mg:

for normal distribution z score =(X-)/ here mean=       = 2.000 std deviation   == 0.30 sample size       =n= 125 std error=x=/n= 0.0268

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