Question

Assume that the weights of Lahontan Cutthroat Trout are normally distributed with a population mean weight...

1. Assume that the weights of Lahontan Cutthroat Trout are normally distributed with a population mean weight of 5 pounds and a standard deviation of 1.2 pounds.
• (a) What is the probability of catching a fish that weighs less than 4.5 pounds?
• (b) What is the probability of catching a fish that weighs greater than 5.25 pounds?
• (c) What is the probability of catching a fish that weighs between 4.5 and 5.25 pounds?

Solution :

Given that ,

mean = = 5

standard deviation = = 1.2

(a)

P(x < 4.5) = P[(x - ) / < (4.5 - 5) / 1.2]

= P(z < -0.42)

= 0.3372

Probability = 0.3372

(b)

P(x > 5.25) = 1 - P(x < 5.25)

= 1 - P[(x - ) / < (5.25 - 5) / 1.2)

= 1 - P(z < 0.21)

= 1 - 0.5832

= 0.4168

Probability = 0.4168

(c)

P(4.5 < x < 5.25) = P[(4.5 - 5)/ 1.2) < (x - ) /  < (5.25 - 5) / 1.2) ]

= P(-0.42 < z < 0.21)

= P(z < 0.21) - P(z < -0.42)

= 0.5832 - 0.3372

= 0.2460

Probability = 0.2460

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