**Statistics and Probability Week 5 Complete Solution**

1. True or False. Justify for full credit.

(a) The normal distribution curve is always symmetric to 0. **Hint: Where is the mean?**

(b) If the variance from a data set is zero, then all the observations in this data set are identical. **Hint: What does variance mean?**

(c) P(AOR A complement) =1, where A complement is the complement of A. **Hint: What does complement mean?**

(d) In a hypothesis testing, if the p-value is less than the significance level α, we do not have sufficient evidence to reject the null hypothesis**.** **https://onlinecourses.science.psu.edu/statprogram/node/138**

(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set. **http://statistics.wikidot.com/ch6**

The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.

**100 + or - sd (15) = 1 sd =? 2 sds = ? 3sds = ? **

2.. What is the probability that a randomly selected person has an IQ between 85 and 115?

3. Find the 90th percentile of the IQ distribution**. Hint: Using a normal table, Probability = .4500**

**Z = 1.645 sd**

4. If a random sample of 100 people is selected, what is the standard deviation of the sample mean?

**standard deviation = sd/n**

5. A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime. Show all work. Just the answer, without supporting work, will receive no credit

**xbar - 1.96 SD/SQRT(100) < mean < xbar +1.96 SD/SQRT(100) where xbar = sample mean**

**xbar = 3000 hours, SD = 500 hours, n = 100**

Use for Questions 1 and 2: A grocery store takes a random sample of 200 customers. The average check-out time is 4 minutes with a standard deviation of two minutes.

1. The standard error of the mean is?

2. The 95% confidence level for the true average check-out time is?

3. A random sample of 244 observations has a mean of 10, a median of 12 and a mode of 33. The population deviation is known to equal 2.8. the 95.44% confidence interval for the population mean is?

4. The following random sample was collected: 22 33 44 6 The 80% confidence interval for the mean is?

5. A random sample of 200 people was taken. Sixty percent of the people favor President Obama. The 95% confidence interval for the true population of people who favor Obama is?

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