Question

According to a study, the random variable, at least X, expressing the length of the fish endemic to a lake follows a normal distribution with mean µ = 20cm and standard deviation σ = 4cm. a) A fish is fishing by the lake. What is the probability that its length is greater than 18cm but does not exceed 24cm? b) Determine a symmetric mean of the X interval whose lengths are 95% of the lake's fish. c) Angling 4 fish from the lake: i) What is the probability that their average length is less than 15cm? ii) What is the probability that at least 3 of them are between 18cm and 24cm in length?

Answer 1