1. Flor is filling up John's food dish for a long trip. Suppose that bags are normally distributed with an average of 35 cups with a standard deviation of 0.5 cups. She uses a scoop that averages 0.75 cups with a standard deviation of 0.25 cups.

Let X be the amount of food in a container remaining after removing two scoops from a bag of food. Determine the expected value for X. Include units.

2.Flor is filling up John's food dish for a long trip. Suppose that bags are normally distributed with an average of 34 cups with a standard deviation of 0.5 cups. She uses a scoop that averages 0.75 cups with a standard deviation of 0.25 cups.

1. Let X be the amount of food in a container remaining after removing two scoops from a bag of food.Determine the standard deviation for X. Include units. Round your answer to at least three decimal places.

3.Recall that the Moderna COVID-19 vaccine is estimated to be 95% effective (95% do NOT get COVID-19 when exposed to it). Suppose now that 500 people are exposed to COVID-19 at a large indoor concert. Let X represent the number of individuals that do not get COVID-19.

Is n large enough to use the normal approximation for X? If so, explain why and determine which normal.

4.A student in a MTH 215 class is in the top 20% for the class with a score of a 85 points on the last exam. Due to an ice cream related incident, the average for the class has been lost and only the standard deviation of 4 points is known.

Knowing this, determine what the class average should be if grades follow a normal distribution. Round your final answer to