3 Complete the following exercises a Supppose you survey 50

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)

Solution

Occurance(X)

Frequency(f)

Freq*X

(X-mean)

(X-mean)2

f*(X-mean)2

38000

6

228000

-12000

144000000

864000000

43000

8

344000

-7000

49000000

392000000

48000

12

576000

-2000

4000000

48000000

53000

12

636000

3000

9000000

108000000

58000

8

464000

8000

64000000

512000000

63000

4

252000

13000

169000000

676000000

Total ->

50

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.

---------------------------------------------------------

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

Occurance(X)	Frequency(f)	Freq*X	(X-mean)	(X-mean)2	f*(X-mean)2
38000	6	228000	-12000	144000000	864000000
43000	8	344000	-7000	49000000	392000000
48000	12	576000	-2000	4000000	48000000
53000	12	636000	3000	9000000	108000000
58000	8	464000	8000	64000000	512000000
63000	4	252000	13000	169000000	676000000
Total ->	50	2500000	-	-	2600000000