Statistics help please, Normal Distributions?

Question

In a normal distribution, find MU whe standard deviation is 6 and 3.75% of the area lies to the leaft of 85.

and just to let you all know I don't know how to. I don't understand it. Thanks.

Answer 1

It's been a while since I've done stats, but I'll give it a shot.

The formula that you need to solve this problem is

z = (y - μ) / σ, where

z represents a z-score
y represents a value
μ (mu) is the UNKNOWN mean
σ (sigma) is the standard deviation

Let's see what values we can plug in. You are given a value of 85 for y and a value of 6 for the standard deviation.

z = (85 - μ) / 6

Now, to figure out z, we look at a table of the z-distribution, which should be in your textbook, or you can find tables online. We are told that 3.75% of the area lies to the left of 85. The 3.75% represents the P-value, or probability. Normally, you are given a z-score and you look up the P-value. In this case, you are given a P-value and need a z-score. Because the area lies to the left, what we want is a z-score that corresponds to a left-tail probability of .0375. Look up .0375 in the table and you will find that the corresponding z-score is -1.78. Now we can plug this into our equation.

-1.78 = (85 - μ) / 6

The rest is basic algebra.

Multiply each side by 6.
-10.68 = 85 - μ

Subtract 85 from each side.
-95.68 = - μ

Multiply each side by -1.
95.68 = μ

And there's your answer.

Answer 2

Cepheid beat me to it...but yes thats the answer i got.

Basically, you have to look at the information you are given, missing, and the link between them. These types of questions are just manipulations of the z-table. The missing info is always linked with the z = (x - u)/sigma equation. You can also be confident in the mu obtained because you know only 3.5% of the area under the normal curve is to the left of your x value of 85. (as you approach mu and larger values, the area under the curve will increase)

Also, sometimes when you use the z-table (or other tables) the probability value you need will not always be there, in this case you'll have to interpolate between values.

Answer 3

ok JJ--- you're searching for the z value that delivers a million.0-0.5-0.0228) it truly is 0.4772. searching that section up on the z table you get a cost of two stdev's and considering this is a one tailed try the propose should be lower than the 199 so 2 = (199-mu)/29 So, fifty 8 = 199-mu and hence the propose mu = 141.

Answer 4

Please do your own homework