Number of nickels needed when only standard deviation is mentioned

In summary, the coin counter manufacturer is looking to find the 98% confidence interval for the average weight of a nickel, with a standard deviation of 150 milligrams. They want to know how many nickels must be weighed to have a margin of error of 15 milligrams. The appropriate sample size formula must be used to determine the necessary number of nickels.
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brunettegurl
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#of nickels needed when only standard deviation is mentioned

A previous study of nickels showed that the the standard deviation of the weight of nickels is 150 milligrams. A coin counter manufacturer wishes to find the 98% confidence interval for the average weight of a nickel. How many nickels does he need to weigh to be accurate within 15 milligrams?

Please help I don't know where to start this question except that I know that it has a standard deviation of 150.
 
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Think this way: "... accurate to within 15 milligrams?" can be interpreted as saying you want to construct a 98% confidence interval for the mean weight, and you want to have a large enough sample size for the margin of error to be 15 milligrams. How large a sample is needed. What sample size formula is appropriate?
 

1. How do you determine the number of nickels needed when only standard deviation is mentioned?

The number of nickels needed can be calculated by dividing the standard deviation by the value of a nickel, which is 5 cents. This will give you the number of standard deviations away from the mean, and you can then round up to the nearest whole number to determine the number of nickels needed.

2. Why is the standard deviation used to determine the number of nickels needed?

The standard deviation measures the variability or spread of a set of data. By using the standard deviation, we can determine how many standard deviations away from the mean a value is, and this can help us determine the number of nickels needed to reach a certain value.

3. What if the standard deviation is negative? How do you calculate the number of nickels needed?

If the standard deviation is negative, it means that the data points are below the mean. In this case, you would still divide the absolute value of the standard deviation by 5 to get the number of standard deviations away from the mean. However, instead of rounding up, you would round down to the nearest whole number to determine the number of nickels needed.

4. Can the standard deviation alone determine the number of nickels needed?

No, the standard deviation cannot determine the number of nickels needed on its own. It is just one factor that is used in the calculation. Other factors such as the mean and the value of a nickel are also needed to determine the number of nickels needed.

5. Is there a specific formula for calculating the number of nickels needed when only standard deviation is given?

Yes, the formula for calculating the number of nickels needed when only standard deviation is given is: number of nickels = standard deviation / value of a nickel. However, this formula assumes that the data follows a normal distribution, and other factors such as the mean and the value of a nickel may also need to be considered depending on the specific situation.

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