a A ranger wants to know the average size of trout taken fro

a) A ranger wants to know the average size of trout taken from a lake. How large a sample must be taken to be able to assert with probability of .99 that the sample mean will not be off by more than .6 inches? Assume the standard deviation is 2.4 inches.

b) A computer company wants to determine what proportion of households intends to purchase PC\'s the next year. How large a sample will be needed to assert with probability of .95 that the samplle proporton will not differ from the true proportion by more than .08?

Show work.

Solution

a. Note that

n = z^2 s^2 / E^2

Here, for 99% confidence, z = 2.57583.

Thus, as s = 2.4 in, E = 0.6 in,

n = 106.15

rounding up,

n = 107 [ANSWER, PART A]