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suppose x is a normal random variable with and find p(x > 105.0). a) 0.9993 b) 0.9994 c) 0.9995 d) 0.0007 e) 0.0006 f) none of the above.

Answer :

The value of the probability p(x > 105.0) for the given normal random variable is found as 0.6915.

Explain the term normal random variable?

  • A randomly distributed variable with a mean of 0 and a standard deviation of 1 is referred to as a standard random variable.
  • The letter Z will always stand in for it.
  • regularly distributed random variable, also known as a with standard deviation, is a continuous random variable which probabilities are defined by the normal distribution of mean and standard deviation.

For the stated question -

The formula for the z score -

z = (x - μ)/σ

In which,

μ = 140  and σ = 20

Put the values-

z = (150 - 140)/20

z = 0.5

p(x > 105.0) = p(z > 0.5)

p(x > 105.0) = 0.6915

Thus, the value of the probability p(x > 105.0) for the given  normal random variable is found as 0.6915.

To know more about the normal random variable, here

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The complete question is-

suppose x is a normal random variable with μ = 140  and σ = 20 and find p(x > 105.0).

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