The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2609 and standard deviation 602. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible. a. Find the probability that the customer consumes less than 2488 calories. b. What proportion of the customers consume over 2743 calories? c. The Piggy award will give out to the 2% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award? calories. (Round to the nearest calorie)
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 **amount** of calories consumed by customers at the Chinese buffet is normally distributed with a mean of 2609 and a standard deviation of 602. One randomly selected customer is observed to determine how many calories \( X \) the customer consumes. Round all answers to four decimal places where possible.
a. Find the probability that the customer consumes less than 2488 calories. [ ]
b. What proportion of the customers consume over 2743 calories? [ ]
c. The Piggy award will be given to the 2% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award? [ ] calories. (Round to the nearest calorie)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b188cbb-8d43-4b5d-bc24-4a026de2aeab%2F01028f83-b3a9-453e-a958-f6e42bf9d5ac%2Fvxxqwi_processed.jpeg&w=3840&q=75)
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