John L.

11/13/13

An L.

11/13/13

An L.

asked • 11/12/131. Find the value of x so that the area under the normal curve between μ and x is .4525 and the value of x is less than μ.

2. Find the value of x so that the area under the normal curve between μ and x is approximately .4800 and the value of x is greater than μ.

More

Hi An,

You didn't provide us with a value of μ or σ, so I'll just leave it as μ and σ in the answer:

1. Since x is less than μ we have a negative z score. The z score which corresponds to a probability of 0.4525 between x and μ is -1.67 (you can find this using a table, or using the excel function "=NORMINV(0.5 - 0.4525, 0, 1)", which computes the z score for an area of 0.4525 between x and μ).

Therefore the desired value of x is:

x = μ - 1.67σ

or if μ = 0 and σ = 1,

x = -1.67

2. I'll leave this one up to you, but its the same as (1), except that you're adding the area to 0.5 in the inverse normal function instead of subtracting it, which will give you a positive z score.

John L.

tutor

Hi An,

Since you didn't provide a value for μ or σ we can't really come up with a value for x, only a z score corresponding to the area you provided. The values for μ and σ should have been provided by your book for the question (or they at least should have given you the information necessary to compute μ and σ).

Report

11/13/13

An L.

Oh, excuse my mistake then,

μ = 200

and σ = 25.

Report

11/13/13

Roman C. answered • 11/12/13

Tutor

4.9
(642)
Masters of Education Graduate with Mathematics Expertise

1. To the left of μ, the area is 0.5, and of that, 0.4525 is between x and μ.

Hence, the area left of x is 0.5 - 0.4525 = 0.0475.

Now you can look up the table of z-scores to get z = -1.67.

Hence x = μ - 1.67σ.

2. Since 0.4800 is between μ and x, the area left of x is 0.5+0.4800 = 0.9800.

Now you can look up the table of z-scores to get z = 2.054.

Hence x = μ + 2.054σ.

Andre W. answered • 11/12/13

Tutor

5
(3)
Friendly tutor for ALL math and physics courses

Remember that P(Z≤µ) = P(Z≥µ) = 0.5.

a) P(Z≤z) = 0.5-0.4525 = 0.0475 ⇒ z=-1.67

b) P(Z≥z) = 0.5+0.48 = 0.98 ⇒ z=2.05

To find x, we need to know the values of µ and σ, since x =μ + zσ.

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

An L.

11/13/13