Suppose that the sick leave taken by the typical worker per year has

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Suppose that the sick leave taken by the typical worker per year has

\mu

= 10,

\sigma

= 2, measured in days. A firm has n = 30 employees. Assuming independence, how many sick days should the firm budget if the financial officer wants the probability of exceeding the number of days budgeted to be less than 20%.

EXPERT ANSWER

Solution,

Given that,

mean = \mu = 10

standard deviation = \sigma = 2

n = 30

\mu\bar x = \mu = 10

\sigma\bar x = \sigma / \sqrtn = 2 / \sqrt30 = 0.37

Using standard normal table,

P(Z > z) = 20%

=1 – P(Z < z ) = 0.20

= P(Z < z ) = 1 – 0.20

= P(Z < 0.84 ) = 0.80

z = 0.84

Using z-score formula

\bar x = z * \sigma\bar x + \mu\bar x

\bar x = 0.84 * 0.37 + 10

\bar x = 10.31 days