A random variable X follows the uniform distribution with a lower limit of 720 and an upper limit of 920. a. Calculate the mean and the standard deviation for the distribution. (Round intermediate calculation for standard deviation to 4 decimal places and final answer to 2 decimal places.) b. What is the probability that X is less than 870?

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pedrocarratore pedrocarratore · Answer 1 · 2019-12-10T09:06:37+01:00

Answer:

a. mean = 820; standard deviation = 57.74

b.0.75 or 75%

Step-by-step explanation:

Lower limit (L) = 720

Upper limit (U) =920

a.The mean of an uniform distribution is given by:

[tex]\mu = \frac{L+U}{2}=\frac{720+920}{2}\\ \mu = 820[/tex]

The standard deviation of an uniform distribution is given by:

[tex]\sigma = \frac{U-L}{\sqrt{12}} = \frac{920-720}{\sqrt{12}}\\\sigma=57.74[/tex]

b. The probaility that X is less 870 is:

[tex]P(X<870) = \frac{870-L}{U-L}= \frac{870-720}{920-720} \\P(X<870) = 0.75\ or\ 75\%[/tex]

raphealnwobi raphealnwobi · Answer 2 · 2022-03-08T12:28:33+01:00

The probability that X is less than 870 is 69.15%.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (x - μ)/σ

where x is raw score, σ is standard deviation and μ is mean

From the question, μ ± σ = (720, 920)

μ - σ = 720 (1)

And:

μ + σ = 920 (2)

Hence:

μ = 820, σ = 100

For x < 870:

z = (870 - 820)/100 = 0.5

P(z < 0.5) = 0.6915

The probability that X is less than 870 is 69.15%.

Find out more on Z score at: https://brainly.com/question/25638875