# Question: If z is the positive number such that the interval

If z is the positive number such that the interval within z standard deviations of the mean contains 50% of a normal distribution, then

a. Explain why this value of z is about 0.67.

b. Explain why for any normal distribution the first and third quartiles equal μ - 0.67σ and μ + 0.67σ.

c. The interquartile range, IQR, relates to σ by IQR = 2 × 0.67σ. Explain why.

a. Explain why this value of z is about 0.67.

b. Explain why for any normal distribution the first and third quartiles equal μ - 0.67σ and μ + 0.67σ.

c. The interquartile range, IQR, relates to σ by IQR = 2 × 0.67σ. Explain why.

**View Solution:**## Answer to relevant Questions

Female heights in North America follow a normal distribution with μ = 65 inches and σ = 3.5 inches. Find the proportion of females who are a. Under five feet. b. Over six feet. c. Between 60 and 70 inches. d. Repeat parts ...A Dutch researcher reads that male height in the Netherlands has a normal distribution with μ = 72.0 inches and σ = 4.0 inches. She prefers to convert this to the metric scale (1 inch = 2.54 centimeters). The mean and ...In a given year, the probability that an adult American female dies in a motor vehicle accident equals 0.0001. a. In a city having 1 million adult American females, state assumptions for a binomial distribution to apply to X ...The National Center for Educational Statistics reported that in 2009 the ACT college placement and admission examination had a mean of 21.1 and standard deviation of 5.1. (Source: Data from ...According to a recent Current Population Reports, the population distribution of number of years of education for self-employed individuals in the United States has a mean of 13.6 and a standard deviation of 3.0. a. Identify ...Post your question