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Find endpoints on a standard normal distribution with the given property. The area between is about 0.88 . Round your answers to three decimal places and place the endpoints in increasing order.

Respuesta :

ajeigbeibraheem

Answer:

-1.555 and 1.555

Step-by-step explanation:

For a standard normal distribution:

P(- Ƶ ≤ Z ≤ Ƶ) = 0.88

The normal distribution on the curve is symmetrical about Z = 0

Thus

P( -Ƶ ≤ Z ≤ 0) = P( 0 ≤ Z ≤ Ƶ)

However;

This implies that:

P( -Ƶ ≤ Z ≤ 0)  +  P( 0 ≤ Z ≤ Ƶ) = 0.88

2P ( 0 ≤ Z ≤ Ƶ)  = 0.88

P( 0 ≤ Z ≤ Ƶ) = 0.44

P(Z ≤ Ƶ) - P( Z ≤ 0) = 0.44

Since P(Z ≤ 0) = 0.50

P(Z ≤ Ƶ) = 0.44 + 0.50

P(Z ≤ Ƶ) =  0.94

From the probability value table

z = 1.555

Thus the endpoints are:

-1.555 and 1.555