For each scenario below, decide if you would draw a normal curve with area in (1) the LEFT tail, (2) the RIGHT tail, or (3) TWO tails.
Question 3 options:
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A fashion designer wants to know how many new dresses women buy each year. A sample of 502 women was taken to study their purchasing habits. Construct the 95% confidence interval for the mean number of dresses purchased each year if the sample mean was found to be 9.3. Assume that the population standard deviation is 1.5.
HINT! Think about how many answers you find for a confidence interval.
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Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0, o= 15. A random sample of 35 people is taken. What is the probability of a random person on the street having an IQ score of at least 95?
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The mean number of words per minute (WPM) read by sixth graders is 86 with a standard deviation of 15. If 44 sixth graders are randomly selected, what is the probability that the sample mean would differ from the population mean by greater than 3 WPM?
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The mean life of a television set is 10.1 years with a standard deviation of 1.3 years. If a sample of 95 televisions is randomly selected, what is the probability that the sample mean would be less than 9.9 years?
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Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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