Question

z is a standard normal random variable. The P(-1.96 z -1.4) equals

	a.	0.4192
	b.	0.0558
	c.	0.8942
	d.	0.475

Suppose f(x) = 1/4 over the range a ≤ x ≤ b, and suppose P(X > 4) = 1/2. What are the values for a and b?

	a.	Cannot answer with the information given.
	b.	0 and 4
	c.	2 and 6
	d.	Can be any range of x values whose length (b − a) equals 4.

The standard deviation of a standard normal distribution

	a.	can be any positive value.
	b.	can be any value.
	c.	is always equal to one.
	d.	is always equal to zero.

Given that z is a standard normal random variable, what is the value of  z if the area to the right of z is 0.9834?

	a.	-2.13
	b.	+2.13
	c.	0
	d.	0.4834

Answer 1

z is a standard normal random variable. The P(-1.96 z -1.4) equals

mean =0 and sd=1 for standard normal random variable

Rcode:

library(tigerstats)
pnormGC(c(-1.96,-1.4),region="between",mean=0,sd=1,graph=TRUE)

Output:

0.05575876

ANSWER;

0.0558

Solution2:

The standard deviation of a standard normal distribution

For z mean=0,sd=1

c.	is always equal to one.

Solution3:

Given that z is a standard normal random variable, what is the value of  z if the area to the right ofz is 0.9834?

Rcode:

library(tigerstats)

pnormGC(bound=-2.13,region="above",mean=0,sd=1,graph=TRUE)

output:

0.9834142

P(Z> -2.13)=0.9834

A) -2.13