(5 pts) The length, X, of a fish from a particular mountain lake in Idaho is normally distributed with \mu = 9.7 inches and \sigma = 1.7 inches.
(a) Is X a discrete or continuous random variable? (Type: DISCRETE or CONTINUOUS)
ANSWER:
(b) Write the event ''a fish chosen has a length of over 8.7 inches'' in terms of X: .
(c) Find the probability of this event:
(d) Find the probability that the length of a chosen fish was greater than 12.2 inches: .
(e) Find the probability that the length of a chosen fish was between 8.7 and 12.2 inches:
continuous, because you can get smaller and smaller intervals.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to each of the Z scores.
jij
234/23
(a) X is a continuous random variable.
Explanation: A continuous random variable can take any value within a particular range, in this case, the length of the fish can be any real number.
(b) The event "a fish chosen has a length of over 8.7 inches" in terms of X can be written as: X > 8.7.
Explanation: This notation represents that the length of the fish, denoted by X, is greater than 8.7 inches.
(c) To find the probability of this event, we need to calculate the area under the normal distribution curve above the value of 8.7 inches.
Explanation: We can find this probability by using the cumulative distribution function (CDF) of the normal distribution.
(d) To find the probability that the length of a chosen fish was greater than 12.2 inches, we need to calculate the area under the normal distribution curve above the value of 12.2 inches.
Explanation: Similar to the previous question, we use the CDF of the normal distribution to find this probability.
(e) To find the probability that the length of a chosen fish was between 8.7 and 12.2 inches, we need to calculate the area under the normal distribution curve between these two values.
Explanation: This probability is obtained by subtracting the probability of X being less than 8.7 inches from the probability of X being less than 12.2 inches.