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The estimated standard deviation from the range rule is 145.5 cm3.As it is 29.8 cm3 smaller than the exact standard deviation, we consider that the estimation is not accurate enough.
Generally, brain volumes which are smaller than 921.1 cm3 can be considered significantly low and bigger than 1417.5 cm3 can be considered significantly high. Hence, brain volume of 1457.5 cm3 is bigger than the expected maximum, so it can be considered significantly high.
The calculation goes like this,
According to the range rule, the standard deviation and range, or the distance between the maximum and smallest value, are roughly inversely proportional:
If we have a sample of 50 brains volumes, and they range from 910 cm3 to 1492 cm3, we can estimate the standard deviation as:
s=1492-910/4=582/4=145.5
The exact standard deviation is 175.3 cm3.The difference is 175.3-145.5=29.8 cm3, so the estimation is not accurate enough.
The range rule of thumb states that we should anticipate a maximum value that is approximately two standard deviations above the mean and a lowest value that is approximately two standard deviations below the mean. The expected ranges are as follows given our mean volume of 1169.3 cm3 and standard deviation of 124.1 cm3:
Min= M-2s=1169.3-2*124.1=921.1
Max=M+2s=1169.3+2*124.1=1417.5
The brain capacity of 1457.5 cm3 can be regarded as significantly high because it is higher than the predicted maximum.
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Answer:
a) 59.98
b) 2.99
c) 2.99
d) Significantly High
Step-by-step explanation:
Part a)
Highest speed measured = x = 75.6 Mbps
Average/Mean speed = = 15.62 Mbps
Standard Deviation = s = 20.03 Mbps
We need to find the difference between carrier's highest data speed and the mean of all 50 data speeds i.e. x -
x - = 75.6 - 15.62 = 59.98 Mbps
Thus, the difference between carrier's highest data speed and the mean of all 50 data speeds is 59.98 Mbps
Part b)
In order to find how many standard deviations away is the difference found in previous part, we divide the difference by the value of standard deviation i.e.
This means, the difference is 2.99 standard deviations or in other words we can say, the Carrier's highest data speed is 2.99 standard deviations above the mean data speed.
Part c)
A z score tells us that how many standard deviations away is a value from the mean. We calculated the same in the previous part. Performing the same calculation in one step:
The formula for the z score is:
Using the given values, we get:
Thus, the Carriers highest data is equivalent to a z score of 2.99
Part d)
The range of z scores which are neither significantly low nor significantly high is -2 to + 2. The z scores outside this range will be significant.
Since, the z score for carrier's highest data speed is 2.99 which is well outside the given range, i.e. greater than 2, we can conclude that the carrier's highest data speed is significantly higher.