The probability that a random student at a university has part-time jobs is 0.6.

Question

The probability that a random student at a university has part-time jobs is 0.6. Choose a random sample of 10 students. a. Find the probability that there are at most 4 students with part-time jobs in the sample. b. Find the probability that there are less than 6 students with part-time jobs, given that there are more than 4 students with part-time jobs in the sample. a. How many ways to arrange letters in B I L L I E? b. How many ways to form a 4-digit code in which the last digit is either 0 or 1? Assume that the digits can be repeated. The commuting time of employees in some company follows Normal distribution with mean of 45 minutes and a standard deviation of 10 minutes. a. What is the probability that a randomly selected employee commutes between 42 and 47 minutes, exclusive?

Explanation / Answer

Answer to the questions as follows:

1.

p = .60
n = 10

a.

P(X<=4)
= 10C0(.60^0)(1-.60)^10 +..+10C4(.60^4)(1-.60)^6
= 0.1662

b.
P(x<6| x>4) = P(X=0,1..5) / P(X=5,6..10) = 0.3669/0.8337 = .44

2a. You can arrange BILLIE in 6!/2!2! = 720/4 = 180 ways
2b. It can be done in 10*10*10*2 = 2000 ways. This is the first 3 places can be filled by any of the 0 to 9

3a. P(42<X<47) = P(42-45 / 10 <Z< 47-45 / 10) = P(-0.3<Z<0.2) = .5793-.3821 = .1972

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