Question

The notation X ~ N (µ, σ) means that the RV X has a normal distribution with mean µ and standard deviation σ. USE A RULER FOR ALL DRAWINGS.

1. What is the z-score of x, when x = 1, and X ~ N (12, 3)?

2. The average score on a math test was 70 points with a standard deviation of 12 points. Jane’s z-score was 2.2. How many points did she score?

3. In 2009, Guinness World Records recognized B. Xishun as the tallest man in the world with a height of x = 2.26 meters. The tallest woman in the world in 2009, M. Dydek, measured y = 2.18 meters. If men heights X ~ N (1.75, 0.15) and women’s heights Y ~ N (1.62, 0.12), compare the relative heights of these individuals using their z-scores. Who would consider the tallest person in the world in 2009? Why? Explain your answer.

Answer 1

1. x = 1

X ~ N(12,3)

So, = 12, and = 3.

                    (Answer)

2. Average score on a math test was 70 points

Standard deviation () of 12 points

Jane’s z-score was 2.2.

We have to find x which is the point scored by Jane.

or, x = 96.4

Therefore, points scored by Jane is 96.4            (Answer)

3. X ~ N (1.75, 0.15)   (Men's Height)

x = 2.26 meters = height of B.Xishun

Therefore, z score of B.Xishun = (2.26-1.75)/0.15 = 3.4

Y ~ N (1.62, 0.12)   (Women's Height)

y = 2.18 metres = height of M.Dydek

Therefore, z score of M.Dydek = (2.18-1.62)/0.12 = 4.67

We can see that height of M.Dydek is 4.67 standard deviations above the mean and height of B.Xinshun is 3.4 standard deviations above the mean.

So, M.Dydek would be considered as the tallest person in the world in 2009 because z score of M.Dydek is more than B.Xinshun.