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L15.2082 - Statistics for Business and Economics (2024/2025)

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A data set containing observations about the "annual wages in a given firm" is:

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A small manufacturing company has 4 workers, each with a different hourly wage. They are:

  1. Worker A: $20 per hour
  2. Worker B: $25 per hour
  3. Worker C: $30 per hour
  4. Worker D: $35 per hour

The company decides to hire a 5th worker to help during the busy season, and this new worker is paid $10 per hour. How hiring the 5th worker will affect the mean and the median of their hourly wages?

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Consider the histogram depicted below:

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In a nationally representative large-scale sample of undergraduate business students was collected data on age, gender, mother's and father's education,  grade in statistics and statistics class attendance (variable equal to 1 if they attended more than 50% of the classes and equal to 0 otherwise).

Students with a higher class attendance had, on average, a higher grade than those with a lower class attendance.

Select the correct option below.

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Consider the Quantile-Quantile (QQ) plot below for the variable `avg_user_rating`.

qqplot

What  does the QQ plot represent? Does it support the use of the normal distribution for modelling `avg_user_rating`? Explain.

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SmartLearn employs a team of 2 helpdesk operators per shift who, together, can resolve a maximum of 20 support tickets (requests) per hour. 

What is the probability that the team is unable to handle all incoming support tickets (requests) during a one-hour period? 

a) Clearly define the random variable and the probability expression.

b) Present your numeric result and provide a brief recommendation to SmartLearn on whether their current staffing is likely to meet demand, or if adjustments may be necessary.

c) Would a normal approximation be appropriate in this case? Justify your answer based on distribution properties.

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