Height (in Inches) Name

72.44 Emma

67.53 Olivia

66.71 Ava

62.02 Isabella

73.89 Sophia

65.95 Mia

65.83 Charlotte

64.15 Amelia

65.39 Evelyn

59.68 Abigail

64.24 Harper

66.60 Emily

65.40 Elizabeth

64.72 Avery

67.11 Sofia

61.97 Ella

62.83 Madison

67.20 Scarlett

66.62 Victoria

68.78 Aria

66.13 Grace

64.47 Chloe

66.64 Camila

62.39 Penelope

63.90 Riley

62.97 Layla

59.31 Lillian

66.14 Nora

67.54 Zoey

63.45 Mila

1. Find Elizabeth in the data and, given the population mean and standard deviation, calculate: a. The z-score for Elizabeth (easiest to be done by hand). b. The probability that a randomly selected female is shorter than Elizabeth. c. The probability that a randomly selected female is taller than Elizabeth. d. Interpret each of these in a sentence (3 full sentences). e. HINT: for this step you should use the mean and standard deviation that are given in the paragraph above "Steps". You should not use a sample mean or sample standard deviation calculated from the data given.

3. As you know, a random sample of 30 women's heights was obtained. Describe the sampling distribution. Use a full sentence here to describe the sampling distribution. HINT: See the Chapter 8 Lecture Notes Key or the Chapter 8 video lecture if you are stuck. You will not use the raw data yet.

4. In StatCrunch or Excel, find and state the mean of the 30 women's heights that were provided (round to two decimal places). Then (using the values from step 3), calculate the probability that a random sample of 30 women's heights would result in a mean that was the value you found or more. Use this probability in a full sentence.

5. Explain how what you just calculated in step 4 relates to the question you were asked in step 2c. Why is the probability in step 4 lower than that in step 2?

6. For this step, please work under the assumption that we do not know the population mean and standard deviation (and in fact, if we are running this test, it means that we are not sure of these values). Construct a 95% confidence interval for the average height of a female. Interpret this confidence interval. HINT: You can use the "with data" option in StatCrunch to use this calculation