There are dozens of species and sub-species of rattlesnakes in the Americas, but

Question

There are dozens of species and sub-species of rattlesnakes in the Americas, but only two in Ohio: the eastern massasauga and the timber rattlesnake. These two, along with the northern copperhead, are the only venomous snakes that naturally occur in the state. It is known that the length of the adult Ohio timber rattlesnake averages 3.7 feet with a standard deviation of 0.45 feet. Suppose that a random sample of 36 adult Ohio timber rattlesnakes was taken.

a. What is the probability that the average length of the 36 randomly selected adult Ohio timber rattlesnakes is less than 3.66 feet?

b. What is the probability that the average length of the 36 randomly selected adult Ohio timber rattlesnakes is between 3.5 and 3.6 feet?

a.0.0874

c. The probability that the average length of the 36 randomly selected adult Ohio timber rattlesnakes is more than k is 9%. Find k.

d. 4.3033

Explanation / Answer

mean = 3.7
std. dev. = 0.45
n = 36

SE = std.dev. / sqrt(n) = 0.45/sqrt(36) = 0.075

a)
P(X < 3.66)
= P(z < (3.66 - 3.7)/0.075)
= P(z < -0.5333 )
= 0.2969

b)
P(3.5 < X < 3.6)
= P((3.5 - 3.7)/0.075 < z < (3.6 - 3.7)/0.075)
= P(-2.6667 < z < -1.3333)
= 0.0874

c)
z-value = 1.3408

xbar = mean + z*SE
xbar = 3.7 + 1.3408*0.075
xbar = 3.8006

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