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DiKsa [7]
3 years ago
13

The Orchard Cafe has found that about 15% of the diners who make reservations don't show up. If 77 reservations have been made,

how many diners can be expected to show up? Find the standard deviation of this distribution
Mathematics
1 answer:
taurus [48]3 years ago
4 0

Answer:

65 dinners are expected to show up

The standard deviation of the distribution is 3.13

Step-by-step explanation:

Given

Proportion = 15%

Population = 77

Required

Expected Number that'll show up

Standard Deviation

<em>If 15% won't show up; then</em>

<em>100% - 15% = 85% will show up</em>

Expected Number, E(x) of Dinner is calculated as thus;

E(x) = np

Where p = 85\% (calculated above)

and n = 77

Convert p to decimal

p = 0.85

So;

E(x) = 0.85 * 77

E(x) = 65.45

E(x) = 65

<em>65 dinners are expected to show up</em>

Calculating Standard Deviation, SD

Standard Deviation is calculated as;

SD = \sqrt{np(1-p)}

Substitute 0.85 for p and 77 for n

SD = \sqrt{77 * 0.85 * (1-0.85)}

SD = \sqrt{77 * 0.85 * 0.15}

SD = \sqrt{9.8175}

SD = 3.13328900678

SD = 3.13 (Approximated)

<em>The standard deviation of the distribution is 3.13</em>

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Read 2 more answers
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