Based on the two samples, what percentage of the people prefer cashew nuts?
Sample 1: 40 almond, 62 pistachio, 63 cashew, 35 walnuts, total 200
Sample 2: 43 almond, 64 pistachio, 61 cashew, 32 walnuts, total 200
A. 62%
B. 30.5%
C. 31.5%
D. 31%
C. 31.5%
Calculations:
In Sample 1, 63 out of 200 people prefer cashew nuts, which is 31.5%.
In Sample 2, 61 out of 200 people prefer cashew nuts, which is 30.5%.
Taking the average of the two percentages gives us 31.5%.
The following data sets represent the highway fuel efficiency in miles per gallon (mpg) of randomly selected cars from two car companies. Which company has cars that are more consistent in highway fuel efficiency?
Car Company A: 35,28,35,30,31,36,35,30
Car Company B: 29,33,40,27,34,34,34,25
To determine which company has cars that are more consistent in highway fuel efficiency, we can calculate the standard deviation of the highway fuel efficiency for each company. A smaller standard deviation indicates less variability and hence more consistency.
For Car Company A:
Mean = (35+28+35+30+31+36+35+30)/8 = 32.5
Calculating the deviations:
Differences from the mean for Car Company A: 2.5, -4.5, 2.5, -2.5, -1.5, 3.5, 2.5, -2.5
Calculating the squared deviations: 6.25, 20.25, 6.25, 6.25, 2.25, 12.25, 6.25, 6.25
Variance = (6.25+20.25+6.25+6.25+2.25+12.25+6.25+6.25)/8 = 8.375
Standard Deviation = √8.375 ≈ 2.896
For Car Company B:
Mean = (29+33+40+27+34+34+34+25)/8 = 31.75
Calculating the deviations:
Differences from the mean for Car Company B: -2.75, 1.25, 8.25, -4.75, 2.25, 2.25, 2.25, -6.75
Calculating the squared deviations: 7.5625, 1.5625, 68.0625, 22.5625, 5.0625, 5.0625, 5.0625, 45.5625
Variance = (7.5625+1.5625+68.0625+22.5625+5.0625+5.0625+5.0625+45.5625)/8 = 18.875
Standard Deviation = √18.875 ≈ 4.344
Comparing the standard deviations:
Car Company A has a standard deviation of approximately 2.896 mpg.
Car Company B has a standard deviation of approximately 4.344 mpg.
Therefore, Car Company A has cars that are more consistent in highway fuel efficiency compared to Car Company B.