Reference no: EM132850220
Every carton of eggs consists of 1 randomly selected cardboard container and 12 randomly selected eggs. The weights of the empty cardboard containers have a mean of 20 grams and a standard deviation of 1.7 grams. The weights of the empty cardboard container and the weights of the eggs are independent. The weights of a full carton have a mean of 840 grams and a standard deviation of 7.9 grams. Let the random variable Y be the weight of a single randomly selected egg.
A: What is the mean of Y?
B: What is the standard deviation of Y?
On paper:
2. Determine if each of the following scenarios are geometric, binomial or neither. (**If geometric or binomial make sure you explain how all conditions are met).
a. A home improvement store advertises that 87% of its sunflower seeds will germinate (grow). Suppose that this claim is true. You buy a packet with 30 sunflower seeds from the store and plant them in your front yard. Let Y = the number of seeds that germinate.
b. Shuffle a standard deck of cards (52 cards). Deal 1 card at a time from the top of the deck until you get an ace. Let T= the number of cards you deal to get an Ace.
c. You are learning to shoot a bow and arrow. On any shot, you have about a 15% chance of hitting the bull's eye. Your instructor makes you keep shooting until you get a bull's eye. Let W = the number of shots it takes for you to hit the bull's eye.
d. A high school football team kicker has made 85% of his field goal attempts. This season he attempts 15 field goals. The attempts differ widely in distance angle, wind and so on. Let X = the number of field goals the kicker makes.
3. Given that the heights of males ages 18-25 (measured in inches) have the distribution N(69.5, 1.5), find each of the following. This notation means that it follows a normal curve, their mean height is 69.5 inches, and their standard deviation is 1.5 inches. Draw a normal curve first and use that to answer the questions. Make sure that you label the x-axis correctly. You will need to find z-scores to answer each of these questions.
1. How tall would an 18 to 25 male have to be in order to be in the 73rd percentile?
2. What proportion of males 18 to 25 are between 68 and 71 inches tall?
3. If a 20-year- old make is 73 inches tall, what percentile would this place him?
4. What is the probability that a randomly selected male (age 18 to 25) is less than 67 inches tall or over 72 inches tall?
5. What can we infer about a man 18 to 25 that is 66 inches tall?