A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.9 years, and standard deviation of 1.7 years. If you randomly purchase one item, what is the probability it will last longer than 11 years?

Q: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.9…

A: Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.08 to the left of…

Q: A particular fruit's weights are normally distributed, with a mean of 600 grams and a standard…

A: Solution: Let X be the fruit’s weight. From the given information, X follows normal distribution…

Q: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.2…

A: Probability will be calculated using z table

Q: The average age of accountants is 43 years, with a standard deviation of 5 years. If an accounting…

A: From the given information,   Mean = 43 Standard deviation = 5 Sample size = 30

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!