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Restaurant Patrons Dine-in restaurants are suffering with low patronage during the Covid-19 pandemic
Restaurant Patrons Dine-in restaurants are suffering with low patronage during the Covid-19 pandemic. During the last week, a particular restaurant served only 40,30, 28, 22, 36,21 and 47 patrons. Assume this follows a normal distribution 0.1 points What statistical distribution applies? O Z table T-table 53 0.1 points What is the daily average number of restaurant patrons ? (Dont overthink this) Type your answer. 54 02 points What is the standard deviation of this week's sample of restaurant patrons? (show 3 dp) Type your answer 55 0:3 points With 95% confidence, what is the minimum number of patrons the restaurant can expect on any night? (Round down) Type your answer 56 0.3 points With 95% confidence, what is the maximum number of patrons the restaurant can expect on any night? (Roundup) Type your answer Submit
Expert Solution
Please refer to the table below:
| x | (x-x?) | (x-x?)2 | |
| 40 | 8 | 64 | |
| 30 | -2 | 4 | |
| 28 | -4 | 16 | |
| 22 | -10 | 100 | |
| 36 | 4 | 16 | |
| 21 | -11 | 121 | |
| 47 | 15 | 225 | |
| Sum | 224 | 0 | 546 |
| x? | 32 | ||
| s | 9.539 |
(52) sample size = n = 7
Since the sample size is less than 30 (n < 30), we will use t distribution.
T table
(53) The daily average number of restaurant patrons is:
x? = Σ x/n
x? = 32
(54) The standard deviation is:
s = [ Σ (x-x?)2/(n-1) ]0.5
s = 9.539
The 95% confidence interval is given by:
C.I. = x? ± (t0.025,7-1 * s/n0.5)
= 32 ± (2.447 * 9.539/70.5)
= 32 ± 8.8224
= (23.1776, 40.8224)
(55) The minimum number of patrons the restaurant can expect on any night is 23.
(56) The maximum number of patrons the restaurant can expect on any night is 41.
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