The factory used to produce 126 articles a day. As a result of retooling, production increased to 189 articles a day. What was t
1 answer:
Answer: The answer is 50%.
Step-by-step explanation: Given that the factory produces 126 articles in a day. After retooling, the production of the articles increased and they started producing 189 articles in a day. We need to calculate the percent increase in labour productivity.
We have,
Percent Increase in labour productivity will be equal to the percent increase in the number of articles.
Increase in the number of articles after retooling = 189 - 126 = 63.
Therefore, percent increase in the number of articles is given by
Thus, the labour productivity increased by 50%.
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Answer:
If 24 items are picked at random, 8% of the time their mean life will be less than 5.156 years.
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
If 24 items are picked at random, 8% of the time their mean life will be less than how many years?
This is the value of X when Z has a pvalue of 0.08. So it is X when Z = -1.405.
By the Central Limit Theorem
If 24 items are picked at random, 8% of the time their mean life will be less than 5.156 years.