Question

The number of shark attacks per year in the US is distributed approximately normal, with mean of 31.8 and standard deviation of 10, according to data obtained from the Florida Museum of Natural History

A.) What percent of years will have fewer than 30 shark attacks?

b.) What percent of years will have fewer than 40 shark attacks?

c.) in 2000,there were 51 shark attacks in the U.S. Is this an unusually high number of attacks?

d.) Determine the number of shark attacks per year that separate the top 2% from the bottom 98%

Answer 1

A)

X ~ N( = 31.8 , = 10)

P(X < 30) = P[Z < (30 - 31.8)/10] = P[Z < -0.18] =  0.4286 = 42.86%

B)

P(X < 40) = P[Z < (40 - 31.8)/10] = P[Z < 0.82] =  0.7939 = 79.39 %

C)

Z score for 51 is = (51 - 31.8)/10 = 1.92

Since the Score is less than +3, it is not unusually high number of attacks

D)

Z score for bottom 98% (98 percentile) is  2.054

The number of shark attacks per year that separate the top 2% from the bottom 98%

=

= 31.8 + 2.054 * 10

= 52.34