Assume that a procedure yields a binomial distribution with a trial repeated n 1

Question

Assume that a procedure yields a binomial distribution with a trial repeated n 11 times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of k = 2 successes given the probability q 0.68 of success on a single trial. Report answer accurate to 4 decimal places) P(X k)- The time it takes me to wash the dishes is uniformly distributed between 9 minutes and 17 minutes What is the probability that washing dishes tonight will take me between 12 and 14 minutes? Give your answer accurate to two decimal places. The probability density of a random variable X is given in the figure below From this density, the probability that X is between 0.14 and 1.1 is The probability density of a random variable X is given in the figure below From this density, the probability that X is at least 1.42 is

Explanation / Answer

1. We need to find P( X = k )

we have k = 2 , n = 11 and p = 0.68

So , P(X = k ) = P( X = 2 ) = 0.0009

2. we need to find P(12 < X < 14 ) = P(X<14) - P(X<12)

= ((14 - 9 ) / ( 17 - 9) ) - ((12 - 9 ) / ( 17 - 9) )

P(12 < X < 14 ) = 0.25

3. We need to find P(0.14 < X < 1.1 ) = P(X<1.1) - P(X<0.14)

= ((1.1 - 0 ) / ( 2 - 0) ) - ((0.14 - 0 ) / ( 2 - 0) )

P(0.14 < X < 1.1 ) = 0.48

4. We need to find P(X > 1.42) = 1- P(X<1.42) = 1 - ((1.42 - 0 ) / ( 2 - 0) ) = 0.29

P(X > 1.42) = 0.29

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