A) Grace Floral shops sells several types of roses for all occasions. It is known that 43% of the tosses that is sold by Grace Floral Shop are Eden Roses. 12 roses are ordered to put in a bouquet. (I) Define the random variable for this situation and list its values. (ii) Stating it's parameter(s), what is the probability distribution of this variable? (iii) state the conditions that influence your choice of distribution. (iv) Calculate the probability taht ay most 2 of the roses were Eden Roses.   B) The number of telephone calls comin into Grace Floral Shop to place orders averages 3 per minute. (I) Define the random variable in this situation and list its values. (ii) Stating its parameter(s) what is the probability distribution of its variable? (iii) Compute the probability that 5 calls will arrive per minute. (iv) Compute the probability that 3 or more calls will arrive in a 3-minute interval?

Imagine that you are training to run a half-marathon and so every week you have 2 intense days, 3 light days, and 2 rest days. On your intense days you run 16 km, on your light days you run 5 km, and on your rest days you do not run. How would you model your miles run per day as a random variable? (Hint: probability distribution)

Company F sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable X represent the number of defects on a fat quarter created by Company F. The following table shows the probability distribution of X. X 0 1 2 3 4 or more Probability 0.58 0.23 0.11 0.05 0.03 If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable Y represent the number of defects on a fat quarter that can be sold by Company F. (a) Construct the probability distribution of the random variable Y. (b) Determine the mean and standard deviation of Y. Show your work.   Company G also sells fat quarters. The mean and standard deviation of the number of defects on a fat quarter that can be sold by Company G are 0.40 and 0.66, respectively. The fat quarters sell for $5.00 each, but are discounted by…

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. (a)  Find the probability that at least 4 flights arrive on time. (b)  Would it be unusual for Southwest to have 3 flights arrive late?(Enter YES or NO)