The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2650 and standard deviation 634. 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. What is the distribution of X? X - N( b. Find the probability that the customer consumes less than 2530 calories. c. What proportion of the customers consume over 3010 calories? d. The Piggy award will given 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)

On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 107 and a standard deviation of 17. Suppose one individual is randomly chosen. Let X = IQ of an individual.b. Find the probability that a randomly selected person's IQ is over 94.  Round your answer to 4 decimal places.c. A school offers special services for all children in the bottom 4% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places.d. Find the 25th and 75th percentiles (a.k.a Q1 and Q3) Round your answers to 2 decimal places.Q1: Q3:

The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 64 minutes and a standard deviation of 16 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person at the hot springs stays longer then 79 minutes. c. The park service is considering offering a discount for the 8% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. d. Find the Inter Quartile Range (IQR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutes

The mean is 146 and the standard deviation is 35. A score of 41 is how many z-scores below the mean?