Consider a uniform distribution from a = 1 to b= 22. (a) Find the probability that x lies between 7 and 12. (b) Find the probability that x lies between 4 and 18. (c) Find the probability that x lies between 6 and 10. (d) Find the probability that x lies between 10 and 19. A Click the icon to see the definition of the uniform distribution. Uniform Distribution A uniform distribution is a continuous probability distribution for a random variable x between two values a and b (a

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Consider a uniform distribution from a =1 to b = 22.
(a) Find the probability that x lies between 7 and 12.
(b) Find the probability that x lies between 4 and 18.
(c) Find the probability that x lies between 6 and 10.
(d) Find the probability that x lies between 10 and 19.
Uniform Distribution
A uniform distribution is a continuous probability distribution for a random variable x
between two values a and b (a < b), where asxsb and all of the values of x are
equally likely to occur. The probability density function of a uniform distribution is
Click the icon to see the definition of the uniform distribution.
(a) The probability that x lies between 7 and 12 is
(Round to three decimal places as needed.)
1
on the interval from x = a to x = b. For any value of x less than a or
y =
b-a
greater than b, y = 0.
(b) The probability that x lies between 4 and 18 is
(Round to three decimal places as needed.)
For two values c and d, where
asc<d<b, the probability that x lies
between c and d is equal to the area
under the curve between c and d, as
shown. So, the area of the central
shaded region equals the probability
(c) The probability that x lies between 6 and 10 is
1
(Round to three decimal places as needed.)
b-a
(d) The probability that x lies between 10 and 19 is
(Round to three decimal places as needed.)
that x lies between c and d.
X
a
d.
Print
Done
Transcribed Image Text:Consider a uniform distribution from a =1 to b = 22. (a) Find the probability that x lies between 7 and 12. (b) Find the probability that x lies between 4 and 18. (c) Find the probability that x lies between 6 and 10. (d) Find the probability that x lies between 10 and 19. Uniform Distribution A uniform distribution is a continuous probability distribution for a random variable x between two values a and b (a < b), where asxsb and all of the values of x are equally likely to occur. The probability density function of a uniform distribution is Click the icon to see the definition of the uniform distribution. (a) The probability that x lies between 7 and 12 is (Round to three decimal places as needed.) 1 on the interval from x = a to x = b. For any value of x less than a or y = b-a greater than b, y = 0. (b) The probability that x lies between 4 and 18 is (Round to three decimal places as needed.) For two values c and d, where asc<d<b, the probability that x lies between c and d is equal to the area under the curve between c and d, as shown. So, the area of the central shaded region equals the probability (c) The probability that x lies between 6 and 10 is 1 (Round to three decimal places as needed.) b-a (d) The probability that x lies between 10 and 19 is (Round to three decimal places as needed.) that x lies between c and d. X a d. Print Done
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