Normal Distribution
Not what you're looking for?
1.) A normal distribution has a mean=60 and a standard deviation=6. Find the following probabilities:
p(X>56)
p(X<70)
p(52<X<68)
p(61<X<75)
2.) A normal distribution has a mean=35 and standard deviation=5. Find the scores associated with the following regions:
a.) the score needed to be in the 43rd percentile.
b.) The score needed to be in the top 15% of the distribution.
c.) the scores that rank off the middle 50% of the distribution.
Purchase this Solution
Solution Summary
The solution includes answers and step-by-step explanations of how to solve the problems, including how to calculate a z-score and how to find a probability using a z distribution table.
Solution Preview
1.) A normal distribution has a mean=60 and a standard deviation=6. Find the following probabilities:
We're going to use z-scores to figure this out. The z-score for a given number x is defined as:
z = (x - mean)/standard deviation
For each of the numbers below, we're going to calculate z, then look at a z distribution table to see what percentage of the area of the z-distribution is below or above the z-score. That area will be the probability that we're looking for.
p(X>56)
z = (56 - 60)/6 = -0.667
Look at the z-distribution table here: http://www.statsoft.com/textbook/sttable.html#z. (If you want to use a distribution table from your textbook, go ahead, just follow the same steps below.) Find the p-value corresponding to z = 0.67. It is 0.2486. That means that the area under the curve between z = 0 and z = 0.67 is 0.2486. It also means that the area under the curve between z = 0 and z = -0.67 is 0.2486.
We are interested in the area under the curve above z = -0.67. We can find that by adding
the area under the curve between z = 0 and z = -0.67 (0.2486) to the area ...
Purchase this Solution
Free BrainMass Quizzes
Terms and Definitions for Statistics
This quiz covers basic terms and definitions of statistics.
Measures of Central Tendency
This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.
Know Your Statistical Concepts
Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.
Measures of Central Tendency
Tests knowledge of the three main measures of central tendency, including some simple calculation questions.