Answer:
a) 68%.
b) 93.3%
c) 61.7%
Step-by-step explanation:
We are asked to find the percentage of data under normal distribution for given boundaries.
a) The percentage of data that are within 1 standard deviation of the mean.
We will use empirical rule to solve our given problem.
Empirical rule states that approximately 68% of the data lies within one standard deviation of the mean, therefore, answer for part (a) would be 68%.
b) Since z-score represents that a data point is how many standard deviation above or below mean.
We need to find [tex]P(z>-1.5)[/tex]. We will use formula [tex]P(z>a)=1-P(z<a)[/tex] to solve our given problem.
[tex]P(z>-1.5)=1-P(z<-1.5)[/tex]
Using normal distribution table, we will get:
[tex]P(z>-1.5)=1-0.06681 [/tex]
[tex]P(z>-1.5)=0.93319[/tex]
[tex]0.93319\times 100\%=93.319\%\approx 93.3\%[/tex]
Therefore, approximately 93.3% of the data is to the right of 1.5 standard deviations below the mean.
c) We need to find [tex]P(z<-0.5)+P(z>0.5)[/tex].
[tex]P(z<-0.5)+P(z>0.5)[/tex]
Since normal distribution is symmetric so both these values will be equal.
[tex]0.30854+0.30854=0.61708[/tex]
[tex]0.61708\times 100\%=61.708\%\approx 61.7\%[/tex]
Therefore, approximately 61.7% of the data set is more than 0.5 standard deviations away from the mean.
Answer:
a) 68%.
b) 93.3%
c) 61.7%
Step-by-step explanation:
#platolivesmatter
Hope this helped :)
