“FunBakery" is a bakery shop that customers can use the facilities to bake cakes. According to the record, the duration a customer spends in the shop follows a normal distribution with mean 140 minutes and standard deviation 18 minutes. (a) What is the probability that a customer stays in the shop for more than 3 hours? (b) There are 15% of all customers would stay in the shop for less than t minutes. Find the value of t. Round up the answer to the next integer. The charge in “FunBakery" is $100 for the first hour and then $1.1 per extra minute. (c) Find the average, median and standard deviation of the amount of money a customer spends in the shop. (d) For a customer stays in the shop for 3 hours, how much he / she needs to pay? (e) There are 15% of all customers would pay less than $k. Find the value of k by using your answer in part (b). (f) Write a simple summary about the spending of a customer in “FunBakery".
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!
“FunBakery” is a bakery shop that customers can use the facilities to bake cakes. According to the record, the duration a customer spends in the shop follows a normal distribution with mean 140 minutes and standard deviation 18 minutes.
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(a) What is the probability that a customer stays in the shop for more than 3 hours?
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(b) There are 15% of all customers would stay in the shop for less than t minutes. Find the value of t. Round
up the answer to the next integer.
The charge in “FunBakery” is $100 for the first hour and then $1.1 per extra minute.
-
(c) Find the average, median and standard deviation of the amount of money a customer spends in the shop.
-
(d) For a customer stays in the shop for 3 hours, how much he / she needs to pay?
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(e) There are 15% of all customers would pay less than $k. Find the value of k by using your answer in
part (b).
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(f) Write a simple summary about the spending of a customer in “FunBakery”.
I need (d) (e) (f) answer
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