The continuous random variable, X , has a Normal distribution with mean 2 and va

Question

The continuous random variable, X, has a Normal distribution with mean 2 and variance 4.

(a) Insert the two numerical values required to make the following expression correct

Z= X - (blank) / (blank) ~N(0,1)

b)Insert the numerical value required to make the following expression correct

P(X < 4) = P(Z< blank)

(c) Using the Statistical Tables, find the following probabilities:

Enter probabilities as decimal numbers (4 decimal places are sufficient).

P(0<X) =

P(0 < X < 4) =

Explanation / Answer

a. P(X<4) = ?

Mean = 2

Variance = 4, Stdev = sqrt(variance) = sqrt(4) = 2

P(X<4) = P(Z< 4-2/2) = P(Z<1) = .8413

P(0<X) = P(0-2 / 2 <Z) = P(-1<Z) = .1587

P(0<X<4) = P(0-2/2 <Z<4-2/2) = P(-1<Z<1) = .6827

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