Please help me, I have know idea how to do this and the assignment is due today!

A manufacturer is producing metal rods, whose lengths are normally distributed with a mean of 75.0cm and a standard deviation of 0.25cm. If 3000 metal rods are produced how many will be between 74.5cm and 75.5 cm in length?

The question is worth4 marks. Thanks in advance

... and Candice and Cherie (yesterday).

=(

Google David Lane normal distribution

http://davidmlane.com/hyperstat/z_table.html

To find the number of metal rods that will be between 74.5 cm and 75.5 cm in length, we need to use the properties of the normal distribution.

First, we need to calculate the z-scores corresponding to the lower and upper limits of the desired range.

The z-score measures the number of standard deviations an observation is from the mean. It is calculated using the formula:

z = (x - μ) / σ

Where:
- x is the value we want to standardize,
- μ is the mean of the distribution, and
- σ is the standard deviation of the distribution.

For the lower limit of 74.5 cm:
z_lower = (74.5 - 75.0) / 0.25

For the upper limit of 75.5 cm:
z_upper = (75.5 - 75.0) / 0.25

Next, we need to look up the probabilities corresponding to these z-scores from the standard normal distribution table. This table provides the area under the normal curve to the left of a given z-score.

Using the table, we can find the probabilities corresponding to the z-scores obtained. Subtracting these two probabilities will give us the proportion or percentage of metal rods that fall within the desired range.

Finally, we multiply the proportion by the total number of metal rods produced to get the approximate number of rods that will be between 74.5 cm and 75.5 cm in length.

Here are the steps in a nutshell:
1. Calculate the z-scores for the lower and upper limits.
2. Look up the corresponding probabilities from the standard normal distribution table.
3. Subtract the probability obtained for the lower limit from the probability obtained for the upper limit to get the proportion.
4. Multiply the proportion by the total number of metal rods (3000) to get the approximate number of rods within the desired range.

By following these steps, you should be able to solve the problem and find the answer.

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