According to a 2016 survey, 6 percent of workers arrive to work between 6:45 A. M. and 7:00 A. M. Suppose 300 workers will be selected at random from all workers in 2016. Let the random variable W represent the number of workers in the sample who arrive to work between 6:45 A. M. and 7:00 A. M. Assuming the arrival times of workers are independent. What is closest to the standard deviation of W?

Question

Mathematics

Rocco Dickerson

16 June, 22:47

According to a 2016 survey, 6 percent of workers arrive to work between 6:45 A. M. and 7:00 A. M. Suppose 300 workers will be selected at random from all workers in 2016. Let the random variable W represent the number of workers in the sample who arrive to work between 6:45 A. M. and 7:00 A. M. Assuming the arrival times of workers are independent. What is closest to the standard deviation of W?

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Bella · Answer 1

Closest standard deviation of W = 4.11

Step-by-step explanation:

Randomly selected workers = n = 300

Probability of workers arriving between 6:45 to 7:00 A. M = p = 6% = 0.06

According to binomial distribution:

mean = μ = n. p

= 300 (0.06) = 18

variance = σ² = n. p (1-p)

= (300) (0.06) (1-0.06)

= (18) (0.94)

= 16.92

standard deviation = σ = 4.11