Salaries for entry-level managers at a restaurant chain are normally distributed with a mean of $44,000 and a standard deviation of $6,500. We randomly survey 10 managers from these restaurants.
- In words, X = ______________.
- X ~ _____(_____, _____)
- In words, ΣX = _____________.
- ΣX ~ _____(_____, _____)
- Find the probability that the managers earn a total of over $400,000.
- Find the 90th percentile for an individual manager's salary.
- Find the 90th percentile for the sum of ten managers' salary.
- If we surveyed 70 managers instead of ten, graphically, how would that change the distribution in part (d)?
- If each of the 70 managers received a $3,000 raise, graphically, how would that change the distribution in part (b)?
OpenStax Statistics, 7.2 The Central Limit Theorem for Sums (Optional), exercise 40