Question

Suppose the number of items you can deliver in a day is a random variable with some unknown distribution with a mean = 35 and a standard deviation of 8. 4.75% of all sample means of 36 days will be less than ?.

Group of answer choices

32.7733

37.2267

35.6033

34.3967

36.27

none of these

33.73

Answer 1

Given that,

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 8 / $\sqrt$ 36 = 8 / 6

P(Z < -1.67) = 0.0475

z = -1.67

$\bar x$ = z * $\sigma$ _{$\bar x$}+ $\mu$ _{$\bar x$} = -1.67 * 8 / 6 + 35 = 37.2267

Answer = 37.2267