Question

Assume the random variable x is normally distributed with mean p= 80 and standard deviation o = 4. Find the indicated probability.
P(67 P(67 (Round to four decimal places as needed.)

Answer 1

This question is incomplete, the complete question is;

Assume the random variable x is normally distributed with mean p = 80 and standard deviation σ = 4.

Find the indicated probability.  P(67 < x < 72)

(Round to four decimal places as needed.)

Answer:

the indicated is 0.0222

Step-by-step explanation:

Given the data in the question;

mean μ = 80

standard deviation σ = 4

p ⇒ P ( x -μ  / σ )

so

P(67 < x < 72) ⇒ P( 67-80 / 4 ) < P( x -μ  / σ )  < P( 72-80 / 4 )

P(67 < x < 72) ⇒ P( -13 / 4 ) < P( x -μ  / σ ) < P( -8 / 4 )

P(67 < x < 72) ⇒ P( -13 / 4  < z < -8 / 4 )

P(67 < x < 72) ⇒ P( -3.25  < z < -2 )

⇒ P( z < -2 ) - P( z < -3.25)

Now from z table;

⇒ 0.02275 - 0.00058

P(67 < x < 72) ⇒ 0.02217 ≈ 0.0222  { four decimal places }

Therefore, the indicated is 0.0222