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 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Frequency | 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
Answer:
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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