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Answer :
This problem is based on the concepts of Normal Distribution and Z-scores in Statistics. To answer parts (a) and (b), Z-scores and the Standard Normal Table are needed to find the relevant probabilities and values. Part (c)'s question about the mean changing is unusual, as it would represent a systemic shift in the data.
The given problem is related to the field of Statistics and specifically, it pertains to a concept called the Normal Distribution. To answer these questions, we have to use Z-scores and the Standard Normal Table.
For part (a), we need to find the probability that the sick-leave time is between 50 and 80 hours. We first calculate the Z-scores for these values and use the Standard Normal Table to find the probabilities. However, without the precise Z-scores and Standard Normal Table, an exact numerical answer can't be provided.
For part (b), we want the sick leave time that is exceeded only 10% of the time. This is equivalent to finding the 90th percentile of the distribution. Again, we would use the Standard Normal Table to find this value but we need exact computations to provide the precise time.
For part (c), asking about a new mean is a bit unusual in this context as changing the mean would essentially represent a different distribution of employee sick leave time. The mean would only change if there were a systemic shift in the data, such as a change in company policy or a public health issue.
This problem is based on the concepts of Normal Distribution and Z-scores in Statistics. To answer parts (a) and (b), Z-scores and the Standard Normal Table are needed to find the relevant probabilities and values. Part (c)'s question about the mean changing is unusual, as it would represent a systemic shift in the data.
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