The number of hours spent studying by students on a large campus in the week before final exams follows a normal distribution with standard deviation 8.4 hours. A random sample of these students is taken to estimate the population mean number of hours studying. a) How large a sample is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 b) Would a larger or smaller sample than that stated in a) be required to guarantee that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.10? c) Would a larger or smaller sample than that state in a) be required to guarantee that the probability that the sample mean differs from the population mean by more than 1.5 hours is less than 0.05?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The number of hours spent studying by students on a large campus in the week before final exams follows a
a) How large a sample is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05
b) Would a larger or smaller sample than that stated in a) be required to guarantee that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.10?
c) Would a larger or smaller sample than that state in a) be required to guarantee that the probability that the sample mean differs from the population mean by more than 1.5 hours is less than 0.05?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
