Answer:
a) The mean is 3.25
b) The standard deviation is 0.433
c) The probability that fawn will weigh exactly 3.7 kg is 0
d) The probability that a newborn fawn will be weigh between 2.9 and 3.5 is 0.4
e) The probability that a newborn fawn will be weigh more than 3.3 is 0.4667
f) The probability that a newborn fawn will be weigh more than P(x > 2.9 | x < 3.7) is 0.6667
g) The 59th percentile is 3.385
Step-by-step explanation:
a) In order to calculate the mean we would have to make the following calculation:
mean = (4 + 2.5) / 2 = 3.25
b) In order to calculate the standard deviation we would have to make the following calculation:
standard deviation = (4 - 2.5) / √(12) = 0.433
c) P(X = 3.7) = 0
d) In order to calculate the probability that a newborn fawn will be weigh between 2.9 and 3.5 we would have to make the following calculation:
P(2.9 < X < 3.5) = (3.5 - 2.9) / (4 - 2.5) = 0.4
e) In order to calculate the probability that a newborn fawn will be weigh more than 3.3 we would have to make the following calculation:
P(X > 3.3) = (4 - 3.3) / (4 - 2.5) = 0.4667
f) P(X > 2.9 | X < 3.7) = P(X > 2.9 and X < 3.7) / P(X < 3.7) = P(2.9 < X < 3.7) / P(X < 3.7) = [(3.7 - 2.9) / (4 - 2.5)] / [(3.7 - 2.5) / (4 - 2.5)] = 0.6667
g) In order to calculate the 59th percentile we would have to make the following calculation:
P(X < x) = 0.59
(x - 2.5) / (4 - 2.5) = 0.59
x = 3.385
