3. Complete the following exercises: a) Supppose you survey 50 fellow students a

ID: 3429918 • Letter: 3

Question

3. Complete the following exercises:

a) Supppose you survey 50 fellow students and find the following responses concerning their estimate of the cost of a four-year education at a private school. Calculate the mean, median mode and standard deviation. What does this tell you about the shape of the distribution?

b) Assuming the price of hotel rooms are normally distributed, with a mean of $175 and a SD = $50, what would be the price of a room, if only 2.5% of the rooms were more expensive (Hint: Z-Scores)

Explanation / Answer

Occurance(X)

Frequency(f)

Freq*X

(X-mean)

(X-mean)2

f*(X-mean)2

38000

228000

-12000

144000000

864000000

43000

344000

-7000

49000000

392000000

48000

576000

-2000

4000000

48000000

53000

636000

3000

9000000

108000000

58000

464000

8000

64000000

512000000

63000

252000

13000

169000000

676000000

Total ->

2500000

2600000000

Answer:

Mean = 50000

Standard Deviation = 7284.314

Variance = 53061224.49

Mode = 46-50 and 51-55 (in 000s)

Median = 25 lies in 46-50000

Hence median = 48000

The frequency increases reaches its peak and decreases.

Hence bell shaped distribution.

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Normal distribution with mu =175 and sigma = 50

only 2.5% are more expensive

i.e.P(Z>z) = 0.025

z=1.96

x = Mean + 1.96 sigma

= 175+50(1.96)

=175+98

= 273

Hence price of the room = 273