6-5 Basic Skills and Concepts Statistical Literacy and Critical Thinking 1. Stan

Question

6-5 Basic Skills and Concepts Statistical Literacy and Critical Thinking 1. Standard Error of the Mean The population of current statistics students has ages with mean and standard deviation . Samples of statistics students are randomly selected so that there are exactly 40 students in each sample. For each sample, the mean age is computed. What does the central limit theorem tell us about the distribution of those mean ages? 2. Small Sample Heights of adult females are normally distributed. Samples of heights of adult females, each of size n 3, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as a normal distribution be- cause the sample size is too small? Explain. 3. Notation The population of distances that adult females can reach forward is normally distributed with a mean of 60.5 cm and a standard deviation of 6.6 cm (from the Federal Aviation Administration). If samples of 36 adult females are randomly selected, what do and , represent, and what are their values? 4. Lottery Numbers In each drawing for the Texas Pick 3 lottery, three digits between 0 and 9 inclusive are randomly selected. What is the distribution of the selected digits? If the mean is calcu- lated for each drawing, can the distribution of the sample means be treated as a normal distribution?

Explanation / Answer

1) central limit says

sample mean follow a normal distribution (a bell curve) even if the original variables themselves are not normally distributed

2) no, sample mean can be treated to follow normal , because height follow normal distribution

hence any sample size will work for normal distribution

is the case where the variable don't follow normal distribution, then it follow normal when n > 30

3) mean = 60.5 cm

sd(Xbar) = sd(X)/sqrt(n) = 6.6/sqrt(36) = 1.1

Please rate

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.