Answer:
the probability that the mean number of pieces in a sample of 28 scoops is more than 350 pieces is approximately 0.0228
Explanation:
To find the probability that the mean number of pieces in a sample of 28 scoops is more than 350 pieces, we can use the normal distribution.
The standard error of the mean for a sample of size 28 is the standard deviation of the population divided by the square root of the sample size, or 16 / sqrt(28) = 2.8.
This means that the distribution of the sample means is approximately normally distributed with a mean of 344 pieces and a standard error of 2.8 pieces.
To find the probability that the sample mean is more than 350 pieces, we can use the cumulative distribution function of the normal distribution. In this case, we want to find the probability that a normally distributed random variable is greater than 350.
Using a normal distribution calculator or table, we can find that the probability that a normally distributed random variable with a mean of 344 and a standard error of 2.8 is greater than 350 is approximately 0.0228.
Therefore, the probability that the mean number of pieces in a sample of 28 scoops is more than 350 pieces is approximately 0.0228.