Question

1. A random variable X has a normal distribution with a mean of 75 and a variance of 9. Calculate P(60 < X < 70.5). Round your answer to 4 decimal places.

2. A random variable X has a uniform distribution with a minimum of -50 and a maximum of -20. Calculate P(X > -25). Round your answer to 4 decimal places.

3.Which of the following statements about continuous random variables and continuous probability distributions is/are TRUE?

I. The probability that a continuous random variable takes a negative value is 0.

II. The probability that any continuous random variable takes a value greater than its mean is 0.5.

III. The probability that a uniformly distributed random variable takes a value less than its mean is 0.25.

IV. The probability that a normally distributed random variable takes a value greater than its mean is 0.997.

Answer 1

Answer:

1.

Given,

Mean = 75

Standard deviation = sqrt(variance)

= sqrt(9)

= 3

P(60 < x < 70.5) = P((60-75)/3 < z < (70.5-75)/3)

= P(-5 < z < -1.5)

= P(z < -1.5) - P(z < -5)

= 0.0668072 - 0 [since from z table]

= 0.0668

2.

Given,

X = U(-50 , 50)

f(x) = 1/(b-a)

= 1 /(50+50)

= 1/100 where as -50 < X < 50

P(X > -25) = f(x) dx

= 1/100 dx

= (x/100) limits -25 to 50

= (50 + 25)/100

= 75/100

= 0.75

Please post the remaining question as separate post. Thank you.