Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) T. P(0 ≤ z ≤ 1.61) =

Answer 1

just google "z score calculator"

go into one the webites that pop up,

and plug in z= 1.61

it gives various associated probabilities, including P(0<z<1.61)= .4463

or use z tables. they're also online or usually in the appendix of any statistics textbook

the probability is the same whether it's 0<z<1.61 or 0</=z</=1.61

Answer 2

Hi Lisa,

Recall that a standard normal distribution has mean 0 and standard deviation 1. Now, we will apply the classic formula for introductory statistics:

z=(x-mu)/sigma

x=value you were given

mu=mean

sigma=standard deviation

Now, you were given two x-values here: 0 and 1.61. We can compute z-scores for both. I’ll use z1 for 0 and z2 for 1.61:

z1=(x1-mu)/sigma

x1=0

mu=0

sigma=1

z1=(0-0)/1

z1=0

Now, for z2:

z2=(x2-mu)/sigma

X2=1.61

mu=0

sigma=1

z2=(1.61-0)/1

z2=1.61

Now, we need to standardize these using the z-table. P(X<0)=P(Z<0). For z1, go to z-table, look for 0 at left, .00 at top:

P(Z<0)=0.5000

Now, we do the same for z2:

P(Z<1.61)=0.9463

Now, because of the standard normal distribution, we know:

P(Z<1.61)=P(X<1.61)=0.9463 and

P(Z<0)=P(X<0)=0.5000

To get the area between them, we need to subtract:

P(0<X<1.61)=P(0<Z<1.61)=0.9463-0.5000

P(0<X<1.61)=0.4463

I hope this helps.