Statistics Questions (can you solve them?):?

Question

I have 3 questions for you guys. Here goes...

1.) The table below provides descriptive statistics on daily stock prices for two companies. Based on this information, which stock is more volatile in relative terms.

MSFT VZ
Mean $30 $40
Std Dev $10 $15

2.) The table below summarizes the monthly income of construction workers in two cities.

Tokyo (yen) Hamburg (euro)
Mean ×420,000 €3,200
Std Dev ×20,000 €100

Who is earning relatively more, a worker making ×460,000 per month in Tokyo or one earning €3,300 per month in Hamburg?

3.) If a variable is normally distributed with a mean of 100 and a standard deviation of 10, we would NOT expect which of the following?

a. About half the data to be less than 100
b. About half the data to exceed 100
c. About 95% of the data to be between 90 and 110
d. Almost all the data to be between 70 and 120

Thanks!

Answer 1

1) Coefficient of Variation (CV) = SD*100/Mean

CV for MSFT = 10*100/30 = 33.33%           (SD=10, mean=30)

CV for VZ = 15*100/40 = 37.50%                 (SD=15, mean=40)

The larger the CV the the larger is the variation.

Therefore, it can be said that VZ is more volatile.

 

2) In case of the worker in Tokyo
x460000 - x420000 = x40000
x40000/x20000 = 2 SD
The worker" income is Mean + 2 SD

In case of the worker in Hamburg
Let E denotes euro
E3300 - E3200 = E100
E100/E100 = 1 SD
The worker" income is Mean + 1 SD

Therefore it can be said that the worker in Tokyo is earning relatively more

 

3) CHOICE (c) is the answer to the question because Mean +/- 1 SD covers 68% of the data according to the Empirical Rule
z1 = (90-100)/10 = - 1
z2 = (110-100)/10 = + 1