1 You’re going to catch a fish in the river. You know that its size is normally distributed with mean 56 inches and standard deviation 7 inches. What is the probability that you catch a fish over 60 inches? What is the probability that you catch a fish less than 50 inches?
Solutions
You can start off by getting the z-score value representing 50 inches. This can be done by taking; z= x-µsd where µ = mean deviation and sd= standard deviation. You will have,
z = 56-607 = -0.57. You should know that P(x<50) is equal to P (z = -0.57).Hence, using the z-score table, get the value which is equivalent to -0.571 and it should be 0.2843. Hence, the probability of catching a fish less than 50 inches will be 0.2843 or P(x<50) = 0.2843.
2 Construct a 95% confidence interval if the sample size is 30, mean is 60 and the standard deviation is 8.
Solution
To construct 95% confidence interval, you can start by getting the degree of freedom (d.f). d.f= (1-0.95)/2 = 0.025. To find the confidence interval (c.i), we need to apply the
