The score of a student on a certain exam is represented by a number between 0 and 1. Suppose that the student passes the exam if this number is at least 0.55. Suppose we model this experiment by a continuous random variable X, the score, whose probability density function is given by

f(x) = { x if 0 <= x < 0.5

5x - 2 if 0.5 <= x <= 1

0 otherwise }

a. What is the probability that the student fails the exam?

b. What is the score that he will obtain with a 50% chance?

c. Compute the 10th and 90th percentiles

Question 1- Suppose that one of every ten cereal boxes has a prize, Out of a shipment of n = 400 cereal boxes, find the probability that there are somewhere between 40 and 46 boxes with prizes. (Hint:use the dishonest coin principle with p = 0.1 to solve for the mean and standard deviation. Remember the probability is a decimal number, round the answer to the nearest hundredth.)

Question 2- A normal distribution has a mean of 30 cm and 47.5% of the data is between 24 and 30 cm. What is the standard deviation. (Put in the number only.)

1.  In a recent report released by Consumer Reports, it was reported that 7 in 10 auto accidents involve a single vehicle (thus, 3 out of 10 involve multiple vehicles). Suppose 15 accidents are randomly selected. Let x = the number of accidents involving a single vehicle.

a. What is the probability that less than 14 accidents involve a single vehicle?

b. What is the mean number of single vehicle accidents? What is the standard deviation?

c. What is the probability at least 2 accidents are multiple vehicle accidents?

Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fulfill each week is 2. (a) What is the probability that in a given week the plant cannot fulfill all the placed orders? (b) Assume the answer to part (a) is 20% (It is not; I just want to make sure that everybody uses the same number for part (b)). Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders?

Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fulfil each week is 2. (a) What is the probability that in a given week the plant cannot fulfil all the placed orders? (b) Assume the answer to part (a) is 20% (It is not; I just want to make sure that everybody uses the same number for part (b)). Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders?

Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fullfil each week is 2. (a) What is the probability that in a given week the plant cannot fulfil all the placed orders? (b) Assume the answer to part (a) is 20% (It is not; I just want to make sure that everybody uses the same number for part (b)). Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders?

Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fulfil each week is 2. (a) What is the probability that in a given week the plant cannot fulfil all the placed orders? (b) Assume the answer to part (a) is 20% (It is not; I just want to make sure that everybody uses the same number for part (b)). Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders

Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fulfil each week is 2. (a) What is the probability that in a given week the plant cannot fulfil all the placed orders? (b) Assume the answer to part (a) is 20% (It is not; I just want to make sure that everybody uses the same number for part (b)). Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders?

Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fulfill each week is 2. (a) What is the probability that in a given week the plant cannot fulfill all the placed orders? (b)Assume the answer to part (a) is 20% (It is not; I just want to make sure that everybody uses the same number for part (b)). Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders?

Two best friends sell cupcakes. They have 3 boxes red velvet , 5 boxes vanilla, 4 boxes chocolate, and 6 peanut butter. Each box they sells for $4.

a)   Define random variable
b)   Determine probability distribution and parameters for the random variable defined in item a.
c)   Suppose that after two hours ten boxes of cupcakes have been purchased. Determine the cumulative distribution function for the number of red velvet purchased
d)   Draw the probability distribution function for the number of red velvet purchased.