The Central Limit Theorem for Sums (Optional) · Exercise 34
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.
(a) In words, X = ______________.
(b) X ~ _____(_____, _____)
(c) In words, ΣX = _____________.
(d) ΣX ~ _____(_____, _____)
(e) Find the probability that the managers earn a total of over $400,000.
(f) Find the 90^th percentile for an individual manager's salary.
(g) Find the 90^th percentile for the sum of ten managers' salary.
(h) If we surveyed 70 managers instead of ten, graphically, how would that change the distribution in part (d)?
(i) 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 34
No hints for this one.
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