The following histogram gives the times taken by a random sample of workers of a company to complete a specific task. An estimate of the mean time taken by this group of workers is:

A. 51.7 min
B. 47.0 min
C. 49.7 min
D. 50.0 min

Consider this question stem for both the current question and question eight:

A sample of ten employees at an auditing firm is randomly selected. The probability that three employees in this sample have an honors' degree is 0.215 while the probability that four employees in this sample have an honors' degree is 0.251. Given that the probability of a success is $p$, determine the value of $p$ approximate to three decimal places.

A. 0.084
B. 0.400
C. 0.854
D. 0.454

The estimate of the mean time taken by the group of workers can be determined by finding the midpoint of each interval on the histogram and multiplying it by the corresponding frequency. Then, sum up these products and divide by the total number of workers.

To find the midpoint of each interval, add the lower and upper limits of each interval and divide by 2. For example, for the first interval, the midpoint is

(40 + 45) / 2 = 42.5.

Next, multiply each midpoint by its corresponding frequency. For example, for the first interval, the product is

42.5 * 3 = 127.5.

Repeat this process for all intervals and sum up the products. For example, for all intervals, the sum of the products is

127.5 + 199 + 355.5 + 346 + 357 + 243.5 + 204 = 1832.5.

Finally, divide the sum by the total number of workers, which is the sum of all frequencies. In this case, the sum of all frequencies is 20.

Therefore, the estimate of the mean time taken by this group of workers is 1832.5 / 20 = 91.625 min.

Since none of the answer options provided match this calculated mean, it is not possible to determine the estimate of the mean time taken by this group of workers from the given options.

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