The ages of two groups of dance students are shown in the following dot plots: A dot plot shows Age in years on the horizontal a
2 answers:
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Answer and Step-by-step explanation: For an exponential distribution, the probability distribution function is:
f(x) = λ.
and the cumulative distribution function, which describes the probability distribution of a random variable X, is:
F(x) = 1 -
(a) <u>Probability</u> of distance at most <u>100m</u>, with λ = 0.0143:
F(100) = 1 -
F(100) = 0.76
<u>Probability</u> of distance at most <u>200</u>:
F(200) = 1 -
F(200) = 0.94
<u>Probability</u> of distance between <u>100 and 200</u>:
F(100≤X≤200) = F(200) - F(100)
F(100≤X≤200) = 0.94 - 0.76
F(100≤X≤200) = 0.18
(b) The mean, E(X), of a probability distribution is calculated by:
E(X) =
E(X) =
E(X) = 69.93
The standard deviation is the square root of variance,V(X), which is calculated by:
σ =
σ =
σ = 69.93
<u>Distance exceeds the mean distance by more than 2σ</u>:
P(X > 69.93+2.69.93) = P(X > 209.79)
P(X > 209.79) = 1 - P(X≤209.79)
P(X > 209.79) = 1 - F(209.79)
P(X > 209.79) = 1 - (1 - )
P(X > 209.79) = 0.0503
(c) Median is a point that divides the value in half. For a probability distribution:
P(X≤m) = 0.5
= 0.5
= 0.5
=
= 0.5
= - 0.5
ln() = ln(0.5)
-0.0143.m = - 0.0693
m = 48.46
Correct answer is 33.1 m.
Use The definition of trigonometric functions. The sine of an angle is the quotient of the opposite side and hypotenuse.
Use The definition of trigonometric functions. The sine of an angle is the quotient of the opposite side and hypotenuse.