Question

1.What type of probability distribution will most likely be used to analyze the number students that successfully transfer in the following problem?
The probability that a single transfer student is accepted to Stanford University is 0.3. If 4 students from the same community college apply, what is the probability that no more than 2 are accepted?

Group of answer choices

a.Poisson distribution

b.binomial distribution

c.none of the above

d.all of the above

2.The Z value is calculated as 1.86 for a selected item in a normally distributed population.  If another item is selected, what is the probability of calculating a larger z value?

3. Four percent of the customers of a mortgage company default on their payments. A sample of eight customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

Answer 1

Q1) We are given here that:
P( accepted ) = 0.3

The number of students who are accepted to stanford could be modelled here as:

This is because each students has an independent and equal probability of being accepted here.

2) Probability of getting a larger z value is computed from the standard normal tables as:
P(Z > 1.86) = 1 - P(Z < 1.86) = 1 - 0.9686 = 0.0314

therefore 0.0314 is the required probability here.

3) P(default) = 0.04

Probability that exactly 2 of the 8 customers defaults is computed here as:

Therefore 0.0351 is the required probability here.