Given a normal distribution with a mean of 120 and a standard deviation of 12, what percentage of values is within the interval 96 to 144

0.9545

Step-by-step explanation:

Given that :

Mean (m) = 120

Standard deviation (s) = 12

what percentage of values is within the interval 96 to 144

P(96 < x < 144)

P(x < 96)

obtain the standardized score (Z) :

Z = (x - m) / s

Z = (96 - 120) / 12 = - 2

p(Z < - 2) = 0.02275 ( Z probability calculator)

P(x < 144)

obtain the standardized score (Z) :

Z = (x - m) / s

Z = (144 - 120) / 12 = 2

p(Z < - 2) = 0.97725 ( Z probability calculator)

p(Z < - 2) - p(Z < 2) = 0.97725 - 0.02275 = 0.9545

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

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step-by-step explanation: