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A normal distribution has a mean of µ = 50 with σ = 10. What proportion of the scores in this distribution are greater than X = 65?
Scores on the SAT form a normal distribution with a mean of µ = 500 with σ = 100. What is the probability that a randomly selected college applicant will have a score greater than 640?
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What percentage of scores in a normal distribution would fall between z-scores of 1 and -2?
3
How do you find normal distribution of z-scores?
z-scores are distributed according to the standard normal distribution. That is, with the parameters: mean 0 and variance 1.
How would you characterize the distribution of scores in a normal distribution?
They are said to be Normally distributed.
When to you use a z scores or t scores?
If the distribution is Gaussian (or Normal) use z-scores. If it is Student's t, then use t-scores.
What percentage of scores fall within -3 and plus 3 standard deviations around the mean in a normal distribution?
99.7% of scores fall within -3 and plus 3 standard deviations around the mean in a normal distribution.
What percentage of scores in a normal distribution would fall between z-scores of 1 and -2?
3
How do you find normal distribution of z-scores?
z-scores are distributed according to the standard normal distribution. That is, with the parameters: mean 0 and variance 1.
How would you characterize the distribution of scores in a normal distribution?
They are said to be Normally distributed.
What proportion of the scores in a normal distribution is approximately between z -1.16 and z 1.16?
Between z = -1.16 and z = 1.16 is approx 0.7540 (or 75.40 %). Which means ¾ (0.75 or 75%) of the normal distribution lies between approximately -1.16 and 1.16 standard deviations from the mean.
When to you use a z scores or t scores?
If the distribution is Gaussian (or Normal) use z-scores. If it is Student's t, then use t-scores.
Intelligence scores follow what kind of distribution?
The IQs of a large enough population can be modeled with a Normal Distribution
What proportion of a normal distribution is located between the two z scores -1.25 and 1.25?
Approx 78.88 % Normal distribution tables give the area under the normal curve between the mean where z = 0 and the given number of standard deviations (z value) to its right; negative z values are to the left of the mean. Looking up z = 1.25 gives 0.3944 (using 4 figure tables). → area between -1.25 and 1.25 is 0.3944 + 0.3944 = 0.7888 → the proportion of the normal distribution between z = -1.25 and z = 1.25 is (approx) 78.88 %
For a normal distribution what z-score value separates the lowest 10 percent of the scores from the rest of the distribution?
-1.28
How do you to get the probability in normal distribution?
You calculate the z-scores and then use published tables.
What kind of graph would you use to show the scores?
When putting the scores in, you use the normal distribution graph, which is the best start.
What percentage of scores fall within -3 and plus 3 standard deviations around the mean in a normal distribution?
99.7% of scores fall within -3 and plus 3 standard deviations around the mean in a normal distribution.
What percentage of scores fall below 7 if the nmean is 8 and standard deviation 2?
Assuming a normal distribution, the proportion falling between the mean (of 8) and 7 with standard deviation 2 is: z = (7 - 8) / 2 = -0.5 → 0.1915 (from normal distribution tables) → less than 7 is 0.5 - 0.1915 = 0.3085 = 0.3085 x 100 % = 30.85 % (Note: the 0.5 in the second sum is because half (0.5) of a normal distribution is less than the mean, not because 7 is half a standard deviation away from the mean, and the tables give the proportion of the normal distribution between the mean and the number of standard deviations from the mean.)
