1.In the game of roulette, a player can place a $6bet on the number 10and have a StartFraction 1 Over 38 EndFractionprobability of winning. If the metal ball lands on 10,the player gets to keep the $6paid to play the game and the player is awarded an additional $210. Otherwise, the player is awarded nothing and the casino takes the player's$6. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?

The expected value is $

The player should expect to lose $

2. The mean incubation time for a type of fertilized egg kept at 100.4F is 20 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day. (a) What is the probability that a randomly selected fertilized egg hatches in less than 19 days? (b) What is the probability that a randomly selected fertilized egg hatches between 18 and 20 days? (c) What is the probability that a randomly selected fertilized egg takes over 21 days to hatch?

3.The times per week a student uses a lab computer are normally distributed, with a mean of 5.8 hours and a standard deviation of 1.4 hours. A student is randomly selected. Find the following probabilities.(a) Find the probability that the student uses a lab computer less than 4 hours per week.(b) Find the probability that the student uses a lab computer between 6 and 8 hours per week.(c) Find the probability that the student uses a lab computer more than 9 hours per week

4.

Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed.

SAT Critical Reading Scores200800450Score mu equals 504sigma equals 110200 less than x less than 450x x y graph

The probability that the member selected at random is from the shaded area of the graph is nothing. (Round to four decimal places as needed.)

5.

Use the normal distribution of SAT critical reading scores for which the mean is 513and the standard deviation is 118. Assume the variable x is normally distributed.

left parenthesis a right parenthesis	What percent of the SAT verbal scores are less than 650?
left parenthesis b right parenthesis	If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 525?

6.Find the z-score that has 64.8% of the distribution's area to its right.

7.Find the z-scores for which 40% of the distribution's area lies between minusz and z.

8.

The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12 fluid ounces and a standard deviation of 0.3 fluid ounce. A drink is randomly selected. (a) Find the probability that the drink is less than 11.9 fluid ounces. (b) Find the probability that the drink is between 11.8 and 11.9 fluid ounces. (c) Find the probability that the drink is more than 12.5 fluid ounces. Can this be considered an unusual event? Explain your reasoning.

Please answer as much as you can!