1. The percent of cats between 24.16 and 35.84 is 95%
2. The percent of cats who are longer than 35.84 is 2.5%
3. The percent of cats shorter than 24.16 inches is 16%
The empirical rule - formula
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
Mean, u = 30 inches
Standard Deviation, s = 2.92 inches
Formula for z-score = (x-u)/s
1. We have to find the percent of cats between 24.16 and 35.84 inches.
24.16, z-score = -2
35.84, z-score = 2
According to the empirical rule,
95% of the data values are within 2 standard deviations of the mean.
So, 95% of the cats are between 24.16 and 35.84 inches.
2. Here, x = 35.84
z=(35.84-30)/2.92
z= 2
According to the Empirical Rule,
95% of the values lie within 2 standard deviations of the mean.
which means 5% of the value lie outside 2 standard deviations and half of these i.e. 2.5% will be above 2 standard deviations.
Hence, 2.5% of of cats who are longer than 35.84 inches.
3. Now, x = 36.22
Using the formula mentioned above, we get:
z= 24.16-30/2.92
z=-2
According to empirical rule,
68% of the values lie within 1 standard deviation of the mean.
i.e., remaining 32% are outside the 1 standard deviation and half of the values i.e. 16% are below 1 standard deviation.
Therefore, we can say that 16% percent of cats shorter than 24.16 inches.
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Given
Find z-scores for x = 24.16 and x = 35.84
Use formula
Find the corresponding percentage from z-score table
The percent of cats between 24.16 and 35.84
The percent of cats who are longer than 35.84
The percent of cats shorter than 24.16 inches
