Statistics Question - Normal Distribution

[Chewy0087]

Statistics Question - Normal Distribution SOLVED

Homework Statement

Hey, the question is shown in the attached document.

Homework Equations

Mean = 79 Standard Deviation = 12

The Attempt at a Solution

I dispise these questions, and I'm failing to grasp them at all.

I've done the first two parts fine, but it's part c I'm struggling on.

I've tried using the z function getting me to;

P (Z $$\leq$$ $$\frac{b}{12}$$ ) - P ( Z $$\leq$$ $$\frac{-a}{12}$$ ) = 0.375

But I've got no idea what I'm doing :/ this question has totally thrown me, all of the methods I've used replacing the 2nd equation into the first have given me useless answers, I can usually do these questions fine, but I'm struggling here, any help would be great!

 

[Chewy0087]

never mind, got it, ridiculously easy AGAIN

 

[Architeuthis Dux]

Hello,

I understand that you are struggling with part c of this question. It seems like you have attempted to use the z-function to solve it, but are unsure of what to do next. Let me guide you through the process.

First, let's review what we know about normal distributions. A normal distribution is a bell-shaped curve that represents a set of data that is evenly distributed around its mean. The mean, in this case, is 79 and the standard deviation is 12. This means that the majority of the data falls within 12 points above or below the mean.

Now, in order to solve part c, we need to find the values of a and b. These values represent the boundaries of the area under the curve that we are looking for. The question states that we need to find the probability of a score falling between 70 and 88. This means that a represents the distance between 79 (the mean) and 70, and b represents the distance between 79 and 88.

To find these values, we can use the formula z = (x - μ) / σ, where x is the score we are looking for, μ is the mean, and σ is the standard deviation. Plugging in the values given in the question, we get:

a = (70 - 79) / 12 = -0.75
b = (88 - 79) / 12 = 0.75

Now, we can use the z-function to find the probability of a score falling between these boundaries. Using the standard normal distribution table, we can find that P (Z ≤ -0.75) = 0.2266 and P (Z ≤ 0.75) = 0.7734. To find the probability of a score falling between these boundaries, we subtract the two values: 0.7734 - 0.2266 = 0.5468.

Therefore, the probability of a score falling between 70 and 88 is 0.5468, or 54.68%.

I hope this explanation helps you understand the process better. Remember, practice makes perfect, so keep practicing and don't get discouraged. Good luck!