1. In a normal distribution with mu = 25 and sigma = 9 what number corresponds to z = -2?

Question

2. Let’s assume you have taken 100 samples of size 49 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 16.

3. Find P(11 < x < 16) when mu = 15 and sigma = 3. Write your steps in probability notation

4.What is the critical z-value that corresponds to a confidence level of 86%

approximately 1.48

approximately 1.55

approximately 1.75

none of these

5. Compute the population mean margin of error for a 95% confidence interval when sigma is 4 and the sample size is 36.

± 1.3066...

± 1.0966...

± 1.7166...

none of these

6. A standard IQ test has a mean of 98 and a standard deviation of 1 We want to be 95% certain that we are within 8 IQ points of the true mean. Determine the sample size.

11

15

16

none of these

Answer 1

1. z = (x - mu)/sigma

x = z * sigma + mu = -2 * 9 + 25 = 7

2. standard deviation of sample = sqrt[pop variance/sample size] = sqrt[16 / 100] = 0.4

3. z = STANDARDIZED VARIABLE

z = (16 - 15)/3 = 0.33

P(z) =  0.630557

z = (11 - 15)/3 = -1.333

P(z) = 0.0912118

P(-1.333 &lt; z &lt; 0.33) = 0.630 - 0.091 = 0.539

4. approximately 1.48

5. margin of error = (z-critical) * sigma/sqrt(n) = 1.96 * 4/sqrt(36) = ± 1.3066.

6. SAMPLE SIZE n = [(z-critical value * s)/B]^2 = [(1.96 * 1) / 8]^2 = 1 PERSON