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Extra resources for A Handbook of Statistics
This issue is easily taken care of by standardizing the variable. This means, we convert the random variable to a z random variable by subtracting the mean of the distribution and dividing by its standard deviation. As a specific example, say we want to find the probability that a normally distributed random variable has a mean of 100 and a standard deviation of 10 and we want to find the probability that X is less than 110. In probability terms P(X<110). 8413. You can do this process in Excel without having to do the extra step of standardizing.
3) The actual number of ounces in a one-gallon bottle of laundry detergent. Discrete. The question asks for the number of ounces in a one-gallon bottle 4) The number of defective parts in a shipment of nuts and bolts. Discrete. Again, this question is asking for the number of defective parts. 5) The number of people collecting unemployment insurance each month. Discrete. Again, it is the number of people. Now that we have a working definition for what a random variable is, we can tie it back into our study of probability by introducing the concept of the probability distribution for a discrete random variable.
4) A sample size of 100 produced the sample mean of 16 with a standard deviation of 3. Compute a 95% confidence interval for the population mean. 2. Compute a 99% confidence interval based on this sample data. 6) A sample of data from car lot had the following consumption of gasoline in gallons. 32, 16, 25, 22, 27, 19, 20. Calculate a 90% confidence interval for the mean daily use of gasoline. 7) Suppose you have selected a sample of data with values: 4,6,3,5,9,3. Construct a 90% confidence interval for the population mean.
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