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Math  /  Data & Statistics

QuestionPoints: 0 of 1
Find the probability of zz occurring in the indicated region of the standard normal distribution. Click here to view page 1 of the standard normal table Click here to view page 2 of the standard normal table. P(0<z<197)=□P(0<z<197)=\square (Round to four decimal places as needed.)

Studdy Solution

STEP 1

1. The standard normal distribution is symmetric around z=0 z = 0 .
2. The standard normal table provides the cumulative probability from the left up to a given z z -score.
3. The probability P(0<z<1.97) P(0 < z < 1.97) can be found by subtracting the cumulative probability at z=0 z = 0 from the cumulative probability at z=1.97 z = 1.97 .

STEP 2

1. Find the cumulative probability for z=1.97 z = 1.97 .
2. Find the cumulative probability for z=0 z = 0 .
3. Subtract the cumulative probability at z=0 z = 0 from the cumulative probability at z=1.97 z = 1.97 .

STEP 3

Look up the cumulative probability for z=1.97 z = 1.97 in the standard normal table.
The cumulative probability for z=1.97 z = 1.97 is approximately 0.9756 0.9756 .

STEP 4

Look up the cumulative probability for z=0 z = 0 in the standard normal table.
The cumulative probability for z=0 z = 0 is 0.5000 0.5000 .

STEP 5

Subtract the cumulative probability at z=0 z = 0 from the cumulative probability at z=1.97 z = 1.97 :
P(0<z<1.97)=0.9756−0.5000=0.4756 P(0 < z < 1.97) = 0.9756 - 0.5000 = 0.4756
The probability is:
0.4756 \boxed{0.4756}

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