# 10 In California, we need more

10

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

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

The mean (¯x) rain intensity: inches (Please show your answer to 1decimal place.)The median rain intensity: inchesThe 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 spendaverage of 12 hours studying for the class. A survey was done on 25students, and the distribution of total study hours per week isbell-shaped with a mean of 14 hours and a standard deviation of 2.5hours.Use the Empirical Rule to answer the following questions.a) 68% of the students spend between hours and hours on Statisticseach week.b) 95% of the students spend between hours and hours on Statisticseach week.c) 99.7% of the students spend between hours and hours on

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 maximumfrequency.

Here , maximum frequency=4

Therefore , the observation corresponding to the maximumfrequency=4 is 1

Therefore , Mode=1

11)

Let ,

By using Empirical Rule ,

Now ,

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

i.e.

Therefore , 68% of the students spend between 11.5 hours and16.5 hours on Statistic each week.

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

i.e.

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

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

i.e.

Therefore , 99.7% of the students spend between 6.5 hours and21.5 hours on Statistic each week.

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