Question

mean is 1250
variance is 120
finding the probability between 970 and 1320
$find p{970 < x < 1320}$
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Answer 1

Although you said the variance is 120, I suspect you meant to say standard deviation. If that's the case, then

P(970 < x < 1320)

= P((970 - 1250)/120 < (x - 1250)/120 < (1320 - 1250)/120)

≈ P(-2.3333 < z < 0.5833)

= P(z < 0.5833) - P(z < -2.3333)

≈ 0.72012 - 0.009815

≈ 0.7104

If you really did mean variance, then

P(970 < x < 1320)

= P((970 - 1250)/√120 < (x - 1250)/√120 < (1320 - 1250)/√120)

≈ P(-25.5604 < z < 6.3901)

= P(z < 6.3901) - P(z < -25.5604)

≈ 1 - 0

≈ 1