The number of suits sold per day at Suit World is shown in the probability distribution below. X 19 20 21 22 23 P(X) 0.2 0.2 0.3 0.2 0.1 Find the mean, variance, and standard deviation of the distribution.
Answers
Step-by-step explanation:
The number of suits sold per day at Suit World is shown in the probability distribution below. X 19 20 21 22 23 P(X) 0.15 0.2 0.32 0.19 0.14 a. Verify that this is a discrete probability distribution. b. Draw a discrete probability graph for the distribution. c. Compute and interpret the mean of the random variable. d. Compute the standard deviation of the random variable.
Answer:
Mean = 20.8,std deviation=1.249,So manager should order 104 suits
Step-by-step explanation:
Step 1: In mathematics, particularly in statistics, there are a variety of mean types. Each mean aids in the summary of a particular set of data, usually serving to assess the overall importance of a certain data set.
mean = ∑(X.P(X))
mean = 19*0.2 + 20*0.2 + 21*0.3 + 22*0.2 + 23*0.1
mean = 20.8
variance
σ2 = ∑(x−μ)2P(x)
σ2 = (19−20.8)2(0.2) + (20−20.8)2(0.2) + (21−20.8)2(0.3) + (22−20.8)2(0.2) + (23−20.8)2(0.1)
σ2 = 1.56
Step 2: The root-mean-square deviation is the square root of the mean of all the squares of all the values of a series derived from the arithmetic mean, and it is represented by the symbol σ.
std deviation
σ = (1.56)^0.5
σ = 1.249
(b) mean = 20.8
20.8*5 = 104 suits required for 5 days
so manager should order 104 suits
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