Plastic drinking straws are manufactured to fit into drinks cartons which have a hole in the top. A straw fits into the hole if the diameter of the straw is less than 3 mm. The diameters of the straws have a normal distribution with mean 2.6 mm and standard deviation 0.25 mm.
- 500 straws are chosen at random. Use a suitable approximation to find the probability that at least 480 straws fit into the holes in drinks cartons.
BECAUSE NO ONE IS ANSWERING MY QUESTION. Im so sorry. I really need your help guys.
I'm removing the duplicates of this question by this particular person. He'd better pray someone answers this one!
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To find the probability that at least 480 straws fit into the holes in drinks cartons, we'll need to use the normal distribution.
Step 1: Standardize the values
First, we need to standardize the values of interest using the given mean and standard deviation. We can use the formula for standardization:
Z = (X - μ) / σ
where Z is the standard score, X is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, we want to find the probability that at least 480 straws fit, so we'll standardize the value 480.
Z = (480 - 2.6) / 0.25
Step 2: Calculate the probability
Once we have the standard score, we can use a standard normal distribution table or a calculator to find the corresponding probability.
The probability of Z being greater than or equal to a certain value can be found by subtracting the cumulative probability from 1.
For example, if we find the cumulative probability of Z = 0.8 and subtract it from 1, we get the probability of Z being greater than or equal to 0.8.
Step 3: Approximation
In this case, we're dealing with a large sample size (500), which allows us to use the normal distribution as an approximation. With a large sample size, the distribution of sample means tends to be normally distributed regardless of the distribution of the population.
So, we can use the standard normal distribution table or a calculator to find the probability. Given the mean and standard deviation of the distribution, we can calculate the standard score and use the cumulative probability function to find the probability.
Using a standard normal distribution table or calculator, the probability can be found as follows:
P(Z ≥ Z-score) = 1 - P(Z ≤ Z-score)
Substituting the values, we get:
P(Z ≥ (480 - 2.6) / 0.25) = 1 - P(Z ≤ 1936)
Note: The standard score (Z-score) in this case would be very large, far beyond the range of the standard normal distribution table. Theoretically, the probability would be extremely close to 1.
However, it's important to consider that this is an extreme case, and given the parameters of the problem, it's highly unlikely that all 500 straws would fail to fit into the holes.
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Post the same problem under two different subjects, one minute apart!!
Stop wasting everyone's time.