High School

If the weight of products is distributed as [tex]N(120 \text{ lb}, 30 \text{ lb})[/tex], what is the probability that the weight of a product is between 115 lb and 118 lb? Provide an answer with three decimal points, such as 0.234.

Answer :

The chance that the weight of the product is between 115 and 118 pounds is approximately 0.064.

In this case, we have:

z = (115 - 120) / 30 = -0.1667

z = (118 - 120) / 30 = -0.0667

Now we need to find the area under the standard normal curve between these two values. We can use a standard normal distribution table or a calculator to find this area.

Using a standard normal distribution table, we can look up the values of -0.1667 and -0.0667 and find the corresponding probabilities. We subtract the smaller probability from the larger one to get the area between the two values.

Using a calculator, we can use the cumulative distribution function (CDF) of the standard normal distribution to find the probability directly.

Either way, we get a probability of approximately 0.0641 or 0.0640, depending on the method used.

To know more about probability here.

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