A company sells sunscreen in 500 milliliter (ml) tubes. In fact, the amount of lotion in a tube varies according to a normal distribution with mean ?=498μ=498 ml and standard deviation ?=5σ=5 ml. Suppose a store which sells this sunscreen advertises a sale for 6 tubes for the price of 5. Consider the average amount of lotion from a SRS of 6 tubes of sunscreen and find: (a) The standard deviation of the average, ?¯x¯ : (b) The probability that the average amount of sunscreen from 6 tubes will be less than 491 ml. Answer:
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 company sells sunscreen in 500 milliliter (ml) tubes. In fact, the amount of lotion in a tube varies according to a
(a) The standard deviation of the average, ?¯x¯ :
(b) The probability that the average amount of sunscreen from 6 tubes will be less than 491 ml.
Answer:
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