Question

The length, X, of a fish from a particular mountain lake in Idaho is normally distributed with mu = 9.5 inches and sigma = 1.9 inches. (a) Is X a discrete or continuous random variable? (Type: DISCRETEE or CONTINUOUS) (b) Write the event "a fish chosen has a length of over 6.5 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 12.5 inches: (e) Find the probability that the length of a chosen fish was between 6.5 and 12 5 inches:

Answer 1

a) X is a continuous random variable. b) The event "a fish chosen has a length of over 6.5 inches" can be written as X > 6.5. c) The probability of this event can be calculated using the normal distribution curve.

Step-by-step explanation:

a) X is a continuous random variable. It represents the length of a fish, which is measured and can take on any value between 0 and infinity.

b) The event "a fish chosen has a length of over 6.5 inches" can be written in terms of X as X > 6.5. This means that the length of the fish is greater than 6.5 inches.

c) To find the probability of this event, we need to find the area under the normal distribution curve to the right of 6.5. This can be calculated using a standard normal table or a calculator and is denoted as P(X > 6.5).

d) The probability that the length of a chosen fish is greater than 12.5 inches is denoted as P(X > 12.5) and can be calculated using the same method as in part c.

e) The probability that the length of a chosen fish is between 6.5 and 12.5 inches can be calculated by finding the area under the normal distribution curve between these two values. This can also be denoted as P(6.5 < X < 12.5).