Bass: The bass in Clear Lake have weights that are normally distributed with a m

Question

Bass: The bass in Clear Lake have weights that are normally distributed with a mean of 2.3 pounds and a standard deviation of 0.8 pounds.

(a) If you catch one random bass from Clear Lake, find the probability that it weighs less than 1 pound? Round your answer to 4 decimal places.


(b) If you catch one random bass from Clear Lake, find the probability that it weighs more than 3 pounds? Round your answer to 4 decimal places.


(c) If you catch one random bass from Clear Lake, find the probability that it weighs between 1 and 3 pounds? Round your answer to 4 decimal places.

Explanation / Answer

We have

= 2.3

= 0.8

We need to calculate z-scores to find the probabilities.

b) P(x>3)

X-

Z = -----

Z = (3-2.3)/0.8 = 0.875

Look up 0.75 in a z-table = 1.15

So the probability of a fish being less than 3 pounds is 77.34% and

The probability that the fish is at least 3 pounds is 1-.7734 = 0.2266 = 22.66%.

c) P(1<x<3)

We already have the value for X=3 --> .7734

We much calculated the value of X=1

Z = (1-2.3)/0.8 = -1.625

Look up -1.75 in a z-table = 0.0401

This is the probability that X<1.

We want the probability that x is between 1 and 3 which we can get by subtracting the two z table values

0.7734 - 0.0401 = .7333

So the probability that the fish will be between 1 and 3 pounds is 73.33%.

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.