Question

1. Which of the following is(are) required condition(s) for a discrete probability function?

∑f(x) = 0

f(x) ≥ 1 for all values of x

f(x) < 0

None of the answers is correct.

2.Let Z be the standard normal random variable. What is P(0<Z<2.50)?

		0.4640
		0.4938
		0.3519
		0.4028
		None of the above

3.

A researcher has collected the following sample data.

	5	12	7	9	5
	6	7	5	13	4

The 90th percentile from Excel Functional work is

		12
		12.1
		12.5
		13
		None of the above

Answer 1

Here the detailed step by step answer of your Question is given below,

Que 1) in this Question the correct option is,

D) None of the above is correct.

Here the required condition(s) for a discrete probability function is ,

TWO Requirements for a discrete Probability distribution:
a) the all probabilities must bet 0 and 1
b) here sum of the probabilities must equal to 1.

The discreate probability are the value that x takes is finite or countable.

So other options are incorrect.

Que 2) .

Let Z be the standard normal random variable. What is P(0<Z<2.50) is 0.4938.

The probability is calculated using Standerd normal z-table.

Que 3) The 90th percentile of given data is 13.

The steps to find the 90th percentile is,

We need to compute the 90% percentile based on the data provided.

Position	X (Asc. Order)
1	4
2	5
3	5
4	5
5	6
6	7
7	7
8	9
9	12
10	13

The next step is to compute the position (or rank) of the 90% percentile. The following is obtained:

The 90th percentile is 12.9 i.e equal to 13. Rounded.

This is traditional method of finding the percentile.

You can use Excel also for finding the percentile,

=PERCENTILE (array, k)

Where ,

k = number of required percentile.

Array is our dataset.

Thank you.