Question

At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. Which of the
following is closest to the proportion of orders that are processed in less than 240 seconds?
А
0.17
B
0.25
0.36
D
083
E
0.95

Answer 1

Answer:

The correct option is;

A. 0.17

Step-by-step explanation:

The given information are;

The mean duration it takes a cashier to process an order, μ = 276 seconds

The standard deviation from the mean, σ = 38 seconds

The z-score of the order processing time of x = 240 seconds is given as follows;

$Z=\dfrac{x-\mu }{\sigma }$

Therefore;

$Z=\dfrac{240-276 }{38 } \approx -0.9474$

The probability

P(z = -0.9474) = 0.17361

Therefore, the proportion of orders which are processed in less than 240 is approximately 0.17361 or 0.17 to two places of decimal.

Answer 2

The closest to the proportion of orders that are processed in less than 240 seconds is 17%

The given parameters;

mean of the number of the distribution, M = 276 seconds

standard deviation of the distribution, d = 38 seconds

In a normal distribution curve, 1 standard deviation below the mean is given as follows;

1 standard deviation below mean = 16% = M - d

                                                                   = 276 s - 38 s = 238 s

the mean of distribution = 50% = 276 s

Let the proportion less than 240 s = x%

238 s --------------------------- 16%

240 s ---------------------------- x%

276 s ------------------------------- 50%

Use interpolation method, to determine the value of x;

$\frac{240 - 238}{276 - 238} = \frac{x- 16}{50-16} \\\\\frac{2}{38} = \frac{x- 16}{34} \\\\\frac{1}{19} = \frac{x- 16}{34} \\\\19(x-16) = 34\\\\19x - 304 = 34\\\\19x = 338\\\\x = \frac{338}{19} \\\\x = 17.78\ \%$

Thus, the closest to the proportion of orders that are processed in less than 240 seconds is 17%

Learn more here: https://brainly.com/question/23418254