Question

1. Xtreme Motorsports tacks sales made throughout the day. Let X be the number of motorcycles sold during the first hour of business on a randomly selected day. The probability distribution of X is as follows. 0 1 2 3 4 Motorcycles sold X: Probability P(X): 0.35 0.3 b 0.05 0.05 a) Find the value of b (1 pt) b) Find the mean of the distribution and interpret in context (3 pts) c) Find the standard deviation of the distribution and interpret in context (3 pts) d) What is the probability that Xtreme Motorsports sells more than 1 motorcycle in the first hour of business? (2 pts)
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Answer 1

Answer:

Explanation:

Given the data:

X ___ : 0____ 1 ___ 2 ____ 3 ____ 4

P(X)__: 0.35_0.3___, b ___0.05_ 0.05

Σp(x) = 1

Hence,

0.35 + 0.3 + b + 0.05 + 0.05 = 1

0.75 + b = 1

b = 1 - 0.75

b = 0.25

The mean :

E(x) = Σ(X * p(x))

E(x) = (0*0.35)+(1*0.3)+(2*0.25)+(3*0.05)+(4*0.05)

E(x) = 0 + 0.3 + 0.5 + 0.15 + 0.2 = 1.15

Standard deviation = sqrt(Var(x))

Var(x) = Σx²p(x) - E(x)

Σx²p(x) = (0^2 * 0.35)+(1^2 * 0.3)+(2^2 * 0.25)+(3^2 * 0.05)+(4^2 * 0.05)

= 2.55 - 1.15

= 1.4

Sqrt(1.4) = 1.183