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6.2 Stuff If the distribution of a random variable x is approximately normal, then x t s n follows a t-distribution. Critical values of t are denoted by tc 6.2 Stuff The t-distribution has the following properties: 1. The t-distribution is bell shaped and symmetric about the mean. 2. The total area under a t-curve is 1 or 100%. 3. The mean, median, and mode of the t-distribution are equal to zero. 4. The t-distribution is a family of curves, each determined by a parameter called the degrees of freedom. When you use a t-distribution to estimate a population mean, the degrees of freedom are equal to one less than the sample size (n – 1). 5. As the degrees of freedom increase, the t-distribution approaches the normal distribution. 6.2 Exercise #18 In a random sample of five people, the mean driving distance to work was 22.2 miles and the sample standard deviation was 5.8 miles. Assume the random variable is normally distributed. Construct a 95% confidence interval for the population mean. 6.2 Exercise #27 In a random sample of 50 people, the mean body mass index (BMI) was 27.7 and the standard deviation was 6.1. Assume the body mass indexes are normally distributed. 6.2 Exercise #28 In a random sample of 15 mortgage institutions, the mean interest rate was 4.99% and the standard deviation was 0.36%. Assume the interest rates are normally distributed. 6.2 Exercise #30 In a recent season, the standard deviation of the yards per carry for all running backs was 1.34. The yards per carry of 20 randomly selected running backs are listed below. Assume the yards per carry are normally distributed. 5.6 4.4 3.8 4.5 3.3 5.0 3.6 3.7 4.8 3.5 5.6 3.0 6.8 4.7 2.2 3.3 5.7 3.0 5.0 4.5