STAT 100Section Week 1 and 2

SAMPLE QUESTION #1Suppose we measure the amount of weight 5 Harvard Football players can bench-press, and we record the following observations (in pounds): 280, 250, 355, 275, 290.

What are the mean, median, and standard deviation for these observations?

 

SAMPLE QUESTION #1

Suppose we measure the amount of weight 5 Harvard Football players can bench-press, and we record the following observations (in pounds): 280, 250, 355, 275, 290.

a) What are the mean, median, and standard deviation for these observations?

 Mean = 290

Median = 280

Standard Deviation = 37.21

 

SAMPLE QUESTION #1

Suppose we measure the amount of weight 5 Harvard Football players can bench-press, and we record the following observations (in pounds): 280, 250, 355, 275, 290.

a) What are the mean, median, and standard deviation for these observations?

 Mean = 290

Median = 280

Standard Deviation = 37.21

 b) What would happen to the mean, median and sd if another player (let’s say the kicker) joined the study and lifted only 220 lbs?

SAMPLE QUESTION #1

Suppose we measure the amount of weight 5 Harvard Football players can bench-press, and we record the following observations (in pounds): 280, 250, 355, 275, 290.

a) What are the mean, median, and standard deviation for these observations?

 Mean = 290

Median = 280

Standard Deviation = 37.21

 b) What would happen to the mean, median and sd if another player (let’s say the kicker) joined the study and lifted only 220 lbs?

The median would be 275+280=277.5

The mean would be 278.33 and the standard deviation would be 45.24

SAMPLE QUESTION #2

Female Heights in US ~ N(μ = 63.8in, σ = 2.5in) [http://en.wikipedia.org/wiki/Human_height]

 

Male Heights in US ~ N(μ = 69.2in, σ = 2.8in) [http://hypertextbook.com/facts/2007/SimasCeckauskas.shtml]

 

a) What is the probability that your male TF is only 68in tall or shorter?

 

b) How tall does your male TF have to be in order to be taller than 90% of the US population?

 

c) Shaquille O’Neal is 85 inches tall. What proportion of the US population is as tall as Shaq (or taller)?

SAMPLE QUESTION #2

Female Heights in US ~ N(μ = 63.8in, σ = 2.5in) [http://en.wikipedia.org/wiki/Human_height]

 

Male Heights in US ~ N(μ = 69.2in, σ = 2.8in) [http://hypertextbook.com/facts/2007/SimasCeckauskas.shtml]

 

a) What is the probability that your male TF is only 68in tall or shorter?

Using the equation from class and the given information for male height in the US, we get:

z-score= (68 – 69.2)/2.8 = -1.2/2.8 = -0.4286

From the z table, 0.4286 corresponds to a 33.36% chance that the male TF is 68in or shorter.

 

b) How tall does your male TF have to be in order to be taller than 90% of the US population?

Here we are working backwards. From the table, we find that 90% corresponds to a z-score =1.28.

Therefore, z-score = (x – 69.2) / 2.8 = 1.28

We can solve for x by rearranging the above equation:

(1.28 * 2.8) + 69.2 = x = 72.78 in

 The male TF needs to be 72.78 inches in order to be taller than 90% of the US population.

c) Shaquille O’Neal is 85 inches tall. What proportion of the US population is as tall as Shaq (or taller)?

Using the equation from class and the given information for male height in the US, we get:

z-score= (85 – 69.2)/2.8 = 15.8/2.8 = 5.642

From the z table, 5.642 corresponds to less than a 0.01% chance that the US population is as tall as Shaq or taller.