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Middle SchoolMathematics 5+3 pts
A water park keeps track of the number of times each visitor goes down water slides during their visit . The data shows the number of times 12 visitors went down a water slide. 4, 22, 16, 10, 11, 20, 20, 12, 6, 3, 11, 1 Create a histogram of this data.
Report25.03.2017
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Given:
12 visitors
Visitor # Frequency of going down a water slide
1 4
2 22
3 16
4 10
5 11
6 20
7 20
8 12
9 6
10 3
11 11
12 1
Pls. see attachment for the histogram.
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Answer:
The number of observations in the data set expected to be below a value of 231 is of 4793.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 195
Standard deviation = 12
The normal distribution is symmetric, which means that 50% of the observations are above the mean and 50% are below.
Proportion of observations below 231:
231 = 195 + 3*12
So 231 is three standard deviations above the mean.
Of the 50% of observations below the mean, all are below 231.
Of the 50% of observations above the mean, 99.7% are between the mean of 195 and three standard deviations above the mean(231).
So, the proportion of observations below 231 is:
Out of 4800:
0.9985*4800 = 4793
The number of observations in the data set expected to be below a value of 231 is of 4793.