what is the probability that at least one scored 650 or better?

Question

math sat scores are normally distributed with mean 500 and standard deviation of 100

ten students are selected at random

what is the probability that at least one scored 650 or better?

 

please I want help with that 

Answer 1

You'll have to use your normal distribution tables to find the probability for any one student to score 650 or above.

 

First find the z score:

 

z = (650 - 500) / 100 = 1.5

 

In other words, scores of 650 or above are at least 1.5 standard deviations above the mean.

 

Now look at the table for z = 1.5. The heading of the table should tell you whether the values are for the area left of the z score or the area right of the z score. Some books will give you both tables. What you want to know is the area above, or to the right of z = 1.5.

 

The total area under the curve is always 1.0. So if your table is only giving you the side you don't want, subtract it from 1 to get the number you do want. I'm looking at a table that gives me 0.93319 for the area left of z = 1.5. So that tells me that my answer is:

 

P(one scored 650 or greater): 1 - .93319 = .06681

 

Now we must calculate it for 2, 3 4, and so on, and add them together.

 

P(two scored ≥ 650) = (.06681)² = .00446

P(three scored ≥ 650) = (.06681)³ = .00029

 

and so on......

 

P(ten scored ≥ 650) = (.06681)¹⁰ = 1.77 x 10^-12

 

∑ = .07159

Answer 2

Hey Kshghoun,

 

Try studying.  Try learning.  You've got a lot of questions up here, which come straight from the limited arsenal of stock boilerplate textbook questions.  These take neither creativity nor intelligence to solve, but they do take effort and time in absorbing the correct way to operate the math.  If that's something you've tried, and have trouble with, then get a tutor.  That will enable you to help yourself.  With the right tutor, you'll get a grasp on the ideas and methods which can be employed to solve the problems you're reproducing here.

 

If on the other hand, you don't want to learn anything, but just want answers, then quit stealing from the pockets of people here who otherwise charge for their time.