Posted: January 29th, 2016

Probability in Mathematics

The probability a copy machine breaks in any given week is .4
a) compute the probability it is broken exactly 3 out of 8 weeks. solution:n(p^(x)q^(n-r)
r
b) If it cost $50 to repair, how much would you expect to spend on repairs over an 8 month period? I do not understand (b)
2. The probability of rolling a 7 or 11 is 2/9. Find the probability that the dice will be rolled 4 times before getting a sum of 7 or 11.
3. The mumps vaccine is effective 80% of the time. If 6 people had the vaccine, what is the probability at least 2 will get the mumps
4. Find p(X greater or equal to 3) ( At least 3 failures before succeeding for the fourth time).
5. Suppose the expected number of bugs on a leaf 2.5 and the number of bugs is well modeled by a geometric distribution. What is the probability a leaf will have at least3 bugs?
6. Customer arrivals at a checkout counter have a poison distribution of an average of 7 per hour
a) Find the probability of no more than 3 customers arrive
b) At least 4 customers arrive

7. The proportion of time a person spends on the phone is given by
f(x)=(3/64)x^2(4-x) 0 less or equal to 4
0 otherwise
Use Tchebychefs theorem to find an interval where the proportion is at least 15/16.
8. The space shuttle can be launched any time between 25 and 45 minutes after the crew boards. Give the density function and use it to compute the probability it will be launched between 30 and 35 minutes after the crew boards
9. In a particular forest, the distance between a randomly selected tree and the next nearest tree is exponentially distributed with a mean of 40 feet.
Given the distribution function as f(b)= integral from 0 to b (1/40)e^-(x/40)dx
a) Find P(x less or equal to 60)
b) Find P(x less or equal 70 given that x is less or equal to 50)
10. The neck sizes of men is normally distributed with a mean of 16 and a standard deviation of 1.2
a) Find the probability a randomly selected man has a neck size between 13.5 and 15,8
b) What % of men have neck sizes greater than 18.3?
c) Find the neck size for which only 8% of men have a neck size below that size

11. The median m of a continuous random variable is that value such that F(m)=.5 Find the median for an exponential distribution with theta =4