a. Let the random variable ? be the number of chips per biscuit. Identify the distribution of ? and write down the value/s of its parameter/s. b. Customers who like chocolate will be happy if the number of chocolate chips is more than the advertised average. What is the probability that the mean number of chips per biscuit is more than six? c. The production will be stopped for maintenance if the mean number of chips per biscuit in a batch is less than four. What is the probability that the production will be stopped for maintenance?
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 quality control manager of Mary’s Bakery is inspecting a batch of chocolate-chip biscuits that has just been baked. When the production is operating correctly, the
a. Let the random variable ? be the number of chips per biscuit. Identify the distribution of ? and write down the value/s of its parameter/s.
b. Customers who like chocolate will be happy if the number of chocolate chips is more than the advertised average. What is the probability that the mean number of chips per biscuit is more than six?
c. The production will be stopped for maintenance if the mean number of chips per biscuit in a batch is less than four. What is the probability that the production will be stopped for maintenance?
d. Verify your answers to parts b. and c. using the appropriate Excel statistical
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