9.assume that a fair coin is tossed 100 times find the probability of observing

Question

9.assume that a fair coin is tossed 100 times find the probability of observing 100 times, find the probablity of observing exactlt 50 heads.

10. Find the probability that in 100 rolls of a fair die, we observed at least 20 threes.

11. A compamy manufactures 60,000 pencils each day, quality control studies have shown that on average 4% of the pencils are dective. A random sample of 500 pencils is selected from each day's production and tested. What is the probablity that in the sample there are a. ate least 12 and no more than 24 defective pencils?

b. 32 or more defective pencils?

Many thanks!

Explanation / Answer

(9)

Modelling this as a Binomial distribution with the following parameters:

n = 100, p = 0.5

Let X be the random variable which denotes the number of heads.

P(X = i) = nCi*pi*(1-p)n-i

So,

P(X = 100) = 100C100*0.5100*(1-0.5)100-100. = 7.89*10-31

and

P(X = 50) = 100C50*0.550*(1-0.5)100-50. = 0.0795

Only 1 question per chegg ques is allowed that is why I have answer only the first question.

Hope this helps !

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