Answer :
Using standard deviation, the maximum possible weight for the items discarded is 28004 ounces.
What is meant by standard deviation?
- The standard deviation is a statistic that describes the degree of volatility or dispersion in a set of numerical values.
- A low standard deviation means that the values tend to be close to the established mean, whereas a large standard deviation suggests that the values exist distributed throughout a greater range.
- A measure of a data set's variance from the mean is referred to as "standard deviation."
- While a high standard deviation indicates that the data are more spread, a low standard deviation suggests that the data are clustered around the mean.
So,
- Mean = 4.5
- Standard deviation = 0.3
(A) P(x > 4.14)
- z = (4.14 - 4.5) / 0.3
- = -1.20
- P(z > -1.20) = P(z < 1.20)
- = 0.8849
(B) P(4.8 < x < 5.04)
- = P (4.8 - 4.5/0.3 < x - μ/σ < 5.04 - 4.5/0.3)
- = P(1 < z < 1.80)
- = P(z < 1.80) - P(z < 1)
- = 0.9641 - 0.8413
- = 0.1228 or 12.28 %
(C) P(x > x) = 0.05
- z value will be, 1.645
- 1.645 = (x - 4.5) / 0.3
- x = 4.9935
(D) P(x < 5.01)
- = (z = x - μ/σ)
- = (5.01 - 4.5) / 0.3 = 1.7
- P(z < 1.70) = 0.9554
- n = 27875/0.9954
- = 28004
Therefore, using standard deviation, the maximum possible weight for the items discarded is 28004 ounces.
To learn more about standard deviation refer to:
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Correct question:
The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces. a. What is the probability that a randomly selected item from the production will weigh at least 4.14 ounces? b. What percentage of the items weighs between 4.8 and 5.04 ounces? c. Determine the minimum weight of the heaviest 5% of all items produced. d. If 27,875 items of the entire production weigh at least 5.01 ounces, how many items have been produced?
