here is a distribution of iq scores 74 79 80 83 83 84 85 86...

-Here is a distribution of IQ scores: 74, 79, 80, 83, 83, 84, 85, 86, 86, 87, 89, 90, 90, 91, 94, 96, 97, 98, 100, 128. What is the standard deviation for this group of scores? (Note. MAKE SURE TO use formula for sample standard deviation) 10.23 74 125.68 11.21 -In the population, IQ scores are normally distributed with a mean μ = 100 and σ = 15. Using this information, answer the following questions: A. What percentage of IQ scores among the population fall between 85 and 115? B. What score identifies the top 4.95% of individuals on IQ (i.e., the 4.95% with the highest IQ)? Hint: you will need to compute z-scores and use the standard normal table to answer these questions. 34.13, 1.65 31.74, 124.75 68.26, 124.75 95, 124.75 -Say you had a sample of 100 students and computed a mean IQ of 88 with a standard error of the mean equal to 3. What would be the 95% confidence interval around the mean of 88? 85 - 115 82.12 - 93.88 85.12 - 91.65 -1.96 - 1.96 -The ___________ is the average distance that sample means are from the mean of the sampling distribution. variance standard error t-ratio F-statistic -All randomly selected samples have the exact same probability of producing a sample statistic (e.g., mean) that represents the population parameter. True or False -Which of the following best describes a probability distribution? the distribution of the frequency of occurrence of each category of a variable observed in a sample the distribution of the frequency of occurrence of each category of a variable for a population the distribution of the calculated probabilities of all possible values of a variable the probability of obtaining a sample that produced an extreme value

Transcript

00:01 Once again, welcome to a new problem.

00:05 This time we're dealing with probability distributions.

00:10 We're dealing with probability distributions.

00:15 And to be specific, we're looking at what you call the normal probability distribution.

00:29 So we're looking at the normal probability distribution.

00:34 And when you think about the normal probability distribution, we have this type of distribution with a mean and standard deviation.

00:50 So within one standard deviation of the mean on both sides, we have 68 % of the data distribution, and within two standard deviations of the mean.

01:07 On both sides of the mean, so z2 and z of negative 2, we have 95 % of the data.

01:19 And then finally, when you look at within three standard deviations of the mean on both sides, so z3 and z negative 3, we have 99 .7 % of the data.

01:38 Also, we have z scores.

01:44 So these ones represent z scores, so x minus m, all over sigma and beyond z score, we also have other types of distribution values.

02:01 For example, we can have a population, and within the population, we select a bunch of samples.

02:13 So the population has a population mean me and the samples that we select, so we select different samples right here.

02:27 So up until the nth sample, so we end up having what we call a sampling distribution, a sampling distribution of sample, so we have a sampling distribution of sample means.

02:50 And the essence of that distribution is the mean of the distribution, which is equivalent to the mean of the sampling distribution of sampling means.

03:01 So if i compute the mean of this distribution, it's approximate to the population mean.

03:10 So it has an approximate value to the population mean and then the standard error is the standard deviation of the sampling distribution of the sample mean so we're looking at a new problem and in this particular problem we're seeing different types of data so we have if we look at the data we have 70 the first one we have 74 and then we have 79, 80 of 83, 83, 84, 85, 86, another 86, 87, 89, 90, 90, 91, 94, 96, 97, 19, 90, 90, 91, 94, 96, 100, and 128, 128, and 128, and 128, and 128, and 128.

04:19 So those are the sample values that we have for iq distribution.

04:24 The first thing we want to do is to determine the standard deviation of that distribution.

04:30 So i'm going to say one, the standard deviation, we have the standard deviation of this distribution.

04:48 S is taking the deviation from the main.

04:54 Summing up that squared sum of squares divide by the degrees of freedom and so the standard deviation that we're going to get in the problem is the same as so we do have a mean of 90 so we have a mean of 90 so we have 1800 over 20 and so this gives us a mean of 90 and using that mean we end up with a standard deviation of 11 .2109.

05:36 So that's the first step.

05:38 The second step to this particular problem is assume bless you that the iq has a normal distribution.

05:49 So the iq happens to have a normal distribution and the mean of that distribution happens to be 100.

06:01 The standard deviation, is equivalent to 15.

06:06 So our goal is to figure out the percentage of iq scores between 85 and 115.

06:15 So assume x is 85.

06:18 So we want to get this percentage.

06:21 So the first thing we're going to do is get the z score.

06:23 So x minus me over sigma.

06:27 This is x is 85 minus mu is 100 over sigma.

06:33 So negative 15 over 15 is negative 1.

06:43 So our z score is negative 1.

06:47 And then when we go back to the z table, we already know that at negative 1 we have 34%.

06:56 So probability that the z score is between negative 1 and 0, that's going to give us an iq score or a percentage of 34 or a point 3 .34 or 34 % so that's the number you're looking at in the specific problems so the specific problems gives you 34 % well actually the iq was 115 so we have to change that the mean was so 85, so 85 and 115.

07:42 So we only did 85, that's 1.

07:47 And then 115 x2 is 115.

07:52 So this 1 2 is going to give us a probability of 0 .34.

08:01 So we have to change this from 0 to positive 1.

08:06 And so we're having 68 % of the data.

08:13 So this is 68 % of the data.

08:16 The mean is 100, so a displacement to one side.

08:19 So this is 0 .68.

08:23 That's what you have right there.

08:26 And this represents 68 % in terms of probabilities...