museum florida history
Urgent help needed with the following problem. Please help me understand this question.?
The number of shark attacks per year in the US is distributed approximately normal, with μ = 31.8 and σ = 10, according to data obtained from the Florida Museum of Natural History.
Determine the number of shark attacks per year that separate the top 2% from the bottom 98%.
Determine the number of shark attacks per year that constitute the middle 80% of shark attacks per year.
Please explain how you arrived at your answers. I need to know how to get these answers. Thanks.
P(X < x) = 0.98
P((X-μ)/σ < (x - 31.8)/10) = 0.98
N_Z((x - 31.8)/10) = 0.98
From standard normal tables, the t-value for 0.98 is 2.054
(that is, a bit over 2 standard deviations)
So
(x - 31.8)/10 = 2.054
x = 31.8 + 20.54 = 52.34
The lower limit of the middle 80% satisfies
P(X < x) = 0.10
and the upper limit of the middle 80% satisfies
P(X < x) = 0.90
That is, the remaining 20% is split evenly above and below the middle 80%
P(X < x) = 0.10
P((X-μ)/σ < (x - 31.8)/10)) = 0.10
N_Z((x - 31.8)/10) = 0.10
From standard normal tables, the t-value for 0.10 is -1.28
(x - 32.1)/10 = -1.28
x = 31.8 - 12.8 = 19.0
You should have no trouble showing that the upper limit of the middle 80% is 44.6
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