The weights of individual nails produced by the 'Hammer 'n Nail' hardware company follow a normal distribution with the average nail weight being 5.1 grams and the standard deviation in nail weight being 1.6 grams. When a nail is produced it is discarded if it weighs more than 8.268 grams. Calculate the probability that a randomly selected nail is not discarded. You may find this standard normal table useful. Give your answer as a decimal to 4 decimal places.

Probability =

ive calculated the z score to be 1.98 but i don't know what to do after this. Please help

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to that Z score. In this case, you are looking for the "area in the larger portion."

but i cant find the proportion for a z-score of 1.98

on the table thingy... do i use 1.90 and 2??

My "table thingy" has Z scores to two decimal places. If you have a 1.90 value, there should also be a 1.98 value. Use that.

soo ive got the porpotion. Do i have to do anything with that or is that my answer???

To calculate the probability that a randomly selected nail is not discarded, we need to find the area under the normal curve to the left of the weight 8.268 grams.

First, we need to convert this weight (8.268 grams) into a z-score, which represents how many standard deviations the value is away from the mean.

The formula to calculate the z-score is:
z = (x - mean) / standard deviation

Using the given values:
mean = 5.1 grams
standard deviation = 1.6 grams
x = 8.268 grams

Calculating the z-score:
z = (8.268 - 5.1) / 1.6
z ≈ 1.93

Now that we have the z-score, we can use a standard normal table (also known as a Z-table) to find the probability.

The z-table gives you the cumulative area from the left of the mean to a specific z-score. In this case, we want to find the area to the left of z = 1.93, which represents the probability that a randomly selected nail weighs less than or equal to 8.268 grams.

Looking up the z-score of 1.93 in the table, we find that the cumulative area is approximately 0.9744.

Therefore, the probability that a randomly selected nail is not discarded is approximately 0.9744 or 97.44% (rounded to 4 decimal places).

Please note that depending on the level of accuracy required, you might need to use more decimal places for the z-score and the resulting probability.