Answer:
3) 2.5%
4) 16%
5) 95%
Step-by-step explanation:
Mean = u = 38.36 inches
Standard Deviation = s = 2.14 inches
Formula for z-score = [tex]\frac{x-u}{s}[/tex]
Question 3)
We have to find what percent of children are taller than 42.64 inches. We can do this by converting 42.64 to z-score.
Here, x = 42.64
Using the formula mentioned above, we get:
[tex]z=\frac{42.64-38.36}{2.14}=2[/tex]
According to the Empirical Rule, 95% of the values lie within 2 standard deviations of the mean. This means 5% of the value lie outside 2 standard deviations and half of these i.e. 2.5% will be above 2 standard deviations.
Therefore, we can say that 2.5% of the children are taller than 42.64 inches.
Question 4)
Here x = 36.22
Using the formula mentioned above, we get:
[tex]z=\frac{36.22-38.36}{2.14}=-1[/tex]
According to empirical rule, 68% of the values lie within 1 standard deviation of the mean. This means, remaining 32% are outside the 1 standard deviation and from these half of the values i.e. 16% are below 1 standard deviation.
Therefore, we can say that 16% of the children are shorter than 36.22 inches.
Question 5)
We have to find what percent of children are between 34.08 and 42.64
34.08 converted to z-score = -2
42.64 converted to z-score = 2
According to the empirical rule, 95% of the data values are within 2 standard deviations of the mean.
So, we can conclude that 95% of the children are between 34.08 and 42.64 inches tall.
