Transcription of Chapter 5: Normal Probability Distributions - Solutions
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Chapter 5: Normal Probability Distributions - Solutions
Chapter 5: Normal Probability Distributions - Solutions Note: All areas and z-scores are approximate. Your answers may vary slightly. Normal Distributions : Finding Probabilities If you are given that a random variable X has a Normal distribution, finding probabilities corresponds to finding the area between the standard Normal curve and the x-axis, using the table of z-scores. The mean (expected value) and standard deviation should be given in the problem. For the Probability that X < b, convert b into a z-score using b . z=.. and use the table to find the area to the left of the z-value. For the Probability that X > a, convert a into a z-score using a . z=.. and use the table to find the area to the right of the z-score. For the Probability that a < X < b (X is between two numbers, a and b), convert a and b into z-scores using a b . z= and z =.. and use the table to find the area between the two z-values.
b.Find the mean of the sampling distribution of sample means. x =63 c.Find the standard deviation of the sampling distribution of sample means. ˙ x = ˙ p n = 11 p 100 =1:1 d.What is the probability that the mean of a sample is greater than $74? (hint: rst nd the z-score) z= ˙ = z= ˙ = ˙ =
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