Question

please solve this problem using Excel step by step need to understand how thr problem is done.

4) Given that z is a standard normal random variable, find z for each situation.

a. The area to the left of z is .9750.

b. The area between 0 and z is .4750.

c. The area to the left of z is .7291.

d. The area to the right of z is .1314.

e. The area to the left of z is .6700.

f. The area to the right of z is .3300.

Answer 1

a. The area to the left of z is 0.9750

Answer: We can use the excel formula to find the value of z corresponding to an area 0.9750. The excel formula is:

Therefore, the area to the left of 1.96 is 0.9750

b. The area between 0 and z is .4750.

Answer: Here we have to find the value of z, knowing that the area between 0 and z is 0.4750.

We know the area less than z = 0.5 + 0.4750 = 0.9750. Now we can use the below excel formula to find the value of z.

Therefore, the area between 0 and 1.96 is 0.4750

c. The area to the left of z is .7291.

Answer: We can use the excel formula to find the value of z corresponding to an area 0.7291. The excel formula is:

Therefore, the area to the left of 0.61 is 0.9750

d. The area to the right of z is .1314.

Answer: Please note the excel gives us only the z-values for the areas to the left of z. Now if the area to the right of z is 0.1314, it means the area to the left of z would be 1 - 0.1314 = 0.8686. Now we can use the excel formula, as:

Therefore, the area to the right of 1.12 is .1314.

e. The area to the left of z is .6700.

Answer: We can use the excel formula to find the value of z corresponding to an area 0.6700. The excel formula is:

Therefore, the area to the left of 0.44 is 0.6700

f. The area to the right of z is .3300.

Answer: Please note the excel gives us only the z-values for the areas to the left of z. Now if the area to the right of z is 0.3300, it means the area to the left of z would be 1 - 0.3300= 0.6700. Now we can use the excel formula, as:

Therefore, the area to the right of 0.44 is 0.3300