A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.7 years, and standard deviation of 4.8 years. If you randomly purchase 7 items, what is the probability that their mean life will be longer than 14 years
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!
A manufacturer knows that their items have a
If you randomly purchase 7 items, what is the probability that their mean life will be longer than 14 years?
Given that,
The standard deviation for the 7 items is,
Solve for the z-value as,
The required probability is,
From the Standard Normal Distribution Table,
Step by step
Solved in 3 steps
