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Statistics and Probability Week 5 Complete Solution
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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.

(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.

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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