a) Grace Floral Shop sells several types of roses for all occasions. It is known that 43% of the roses 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 its parameter(s), what is the probability distribution of this variable? (iii) State the conditions that influence your choice of distribution. (iv) Calculate the probability that at most 2 of the roses were Eden Roses. b) The number of telephone calls coming 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 this 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?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Question 3
a) Grace Floral Shop sells several types of roses for all occasions. It is known that 43% of the roses 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 its parameter(s), what is the probability distribution of this variable?
(iii) State the conditions that influence your choice of distribution.
(iv) Calculate the probability that at most 2 of the roses were Eden Roses.
b) The number of telephone calls coming 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 this 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?
Question 4
The time taken by employees at Grace Floral shop to put a bouquet together has a
(i) Find the probability that an employee chosen at random takes between 24.6 and 27.8 minutes to put a bouquet together.
(ii) 12% of employees take more than t minutes to put a bouquet together.
(ii) Find the value of t.
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