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# s2 watch

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1. im stuck on these 2 questions i would be very grateful if someone could help

the sample mean of 9 screws is 8.01mm assuming a normal distribution with variance 0.0001 test at the 5% sig level the hypothesis that the pop mean is 8 against the alternative hypothesis that the pop mean is not 8.

this is what i did
(8.01-8) / sqrt(0.0001/9) =3 but i should get the test statistic z=2 can you see where ive gone wrong?

also a computer is programmed to generate random digits between 0 and 9 inclusive. 400 pairs of random digits are generated what is the probability that there are exactly 3 pairs of zeros amongst them? i tried using a normal approximation but it went weird

thanks
2. i think that you are right (providing this is the population variance) - but this is really an s3 question - in the formula book its says ((x-bar)-mu)/(sqrt(variance/n)) ~N(0,1) so i would say you were right
3. anyone?
4. (Original post by sarah12345)
the sample mean of 9 screws is 8.01mm assuming a normal distribution with variance 0.0001 test at the 5% sig level the hypothesis that the pop mean is 8 against the alternative hypothesis that the pop mean is not 8.

this is what i did
(8.01-8) / sqrt(0.0001/9) =3 but i should get the test statistic z=2 can you see where ive gone wrong?
I think you're right.
(Original post by sarah12345)
also a computer is programmed to generate random digits between 0 and 9 inclusive. 400 pairs of random digits are generated what is the probability that there are exactly 3 pairs of zeros amongst them? i tried using a normal approximation but it went weird
P(a pair of random digits are both zero) = (1/10)^2 = 1/100

Let X be the number of pairs of zeros among the 400 pairs generated. Then X ~ Bin(400, 1/100). Since "n is large and p is small," we can approximate Bin(400, 1/100) by Po(4).

P(X = 3)
= e^(-4) 4^3/3!
= 0.195
5. Thanks alot!!

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