Question

10

In California, we need more rain to sustain the health of our natural environment, argriculture, and economic. A group of statistics students in Oxnard College recorded the amount of rain during 2016-2017 school year, measuring the intensity by the inches of rain, and the results were:

Inches of Rain	1	2	3	4	5	6
Frequency	4	2	3	2	0	3

The mean (¯x) rain intensity: inches (Please show your answer to 1 decimal place.)

The median rain intensity: inches

The mode rain intensity: inches (Please separate your answers by ',' in bimodal situation. Enter DNE if there is no mode.)

11

For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 25 students, and the distribution of total study hours per week is bell-shaped with a mean of 14 hours and a standard deviation of 2.5 hours.

Use the Empirical Rule to answer the following questions.

a) 68% of the students spend between hours and hours on Statistics each week.

b) 95% of the students spend between hours and hours on Statistics each week.

c) 99.7% of the students spend between hours and hours on

Answer 1

10)

Inches of Rain(x)	Frequency(f)	Cummulative Frequency	x*f
1	4	4	1*4=4
2	2	4+2=6	2*2=4
3	3	6+3=9	3*3=9
4	2	9+2=11	4*2=8
5	0	11+0=11	5*0=0
6	3	11+3=14	6*3=18
Total	N=14		43

The mean rain imtensity is ,

inches

The median is the observation corresponding to

Here , N/2=14/2=7

Therefore ,

Therefore , the observation corresponding to c.f.=9 is 3

Therefore , Median=3 inches.

The mode is the observation corresponding to the maximum frequency.

Here , maximum frequency=4

Therefore , the observation corresponding to the maximum frequency=4 is 1

Therefore , Mode=1

11)

Let ,

By using Empirical Rule ,

Now ,

i) The 68% of the students send between one standard deviation of the mean

i.e.

Therefore , 68% of the students spend between 11.5 hours and 16.5 hours on Statistic each week.

ii) The 95% of the students send between two standard deviation of the mean

i.e.

Therefore , 95% of the students spend between 9 hours and 19 hours on Statistic each week.

iii) The 99.7% of the students send between three standard deviation of the mean

i.e.

Therefore , 99.7% of the students spend between 6.5 hours and 21.5 hours on Statistic each week.