the weight of written reports produced in a certain department has a normal distribution with mean 60 grams and standard deviation 12 grams. what is the probability that the next report will weigh less than 45 grams?

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15-12-2022
Mathematics

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the weight of written reports produced in a certain department has a normal distribution with mean 60 grams and standard deviation 12 grams. what is the probability that the next report will weigh less than 45 grams?

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PratikshaS PratikshaS · Answer 1 · 2022-12-21T10:44:54+01:00

The probability that the next report will weigh less than 45 grams = 0.106

In this question, we have been given the weight of written reports produced in a certain department has a normal distribution with mean 60 grams and standard deviation 12 grams.

We need to find the probability that the next report will weigh less than 45 grams.

We have mean= 60 grams

Standard Deviation = 12 grams

First we convert 45 to z score.

45 converted to z score for given mean and standard deviation will be:

z = (45 - 60)/12

z = -1.25

So, from standard normal table a P-value:

P(x<45) = 0.10565

Therefore, the probability would be 0.10565

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