Question

Let the random variable X follow a normal distribution with µ = 19 and σ2 = 8. Find the probability that X is greater than 11 and less than 15.

Answer #1

Solution :

Given that ,

mean = = 19

variance = = 8

standard deviation = = 2.8284

P(x > 11) = 1 - P(x < 11)

= 1 - P((x - ) / < (11 -19) / 2.8284)

= 1 - P(z < -2.83)

= 1 - 0.0023

= 0.9977

Probability = 0.9977

P(x < 15) = P((x - ) / < (15 19) / 2.8284)

= P(z < -1.41)

= 0.0793

Probability = 0.0793

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For
Questions 6 - 8, let the random variable X follow a Normal
distribution with variance σ2 = 625.
Q6. A random sample of n = 50 is obtained with a sample mean, X-Bar
of 180.
What is
the probability that population mean μ is greater than 190?
a.
What is Z-Score for μ greater than 190 ==>
b.
P[Z > Z-Score] ==>
Q7. What
is the probability that μ is between 198 and 211?
a. What
is Z-Score1 for...

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35 b. between 41 and 50
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16?________

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