Do these problems by hand. For each probability from the Normal distribution, dr

Question

Do these problems by hand. For each probability from the Normal distribution, draw a Normal curve and shade the region representing probability of interest. Do not use the same Normal curve for multiple probabilities, only one probability should be represented on each plot. A landscaping maintenence crew cuts the lawn of a large account once each week. The amount of time the crew spends cutting the lawn is a random variable following a Normal distribution with = 3 hours and = 0.3 hours. Find the probabilities that during a randomly selected week, the crew takes: [a.] At least 2.75 hours. [b.] Between 2.5 hours and 3.2 hours.

Explanation / Answer

HERE WE HAVE MEAN = 3

STANDARD DEVIATION = 0.3

Z = (X-MEAN)/STANDARD DEVIATION

A) P(X>2.75) =

For x = 2.75, the z-value z = (2.75 - 3) / 0.3 = 0.83
Hence P(x > 2.75) = P(z > 0.83) = [total area] - [area to the left of 0.83]

= 1 - 0.7967 = 0.2033

B)

For x = 2.5 , z = (2.5 - 3) / 0.3 = -1.66 and for x = 3.2, z = (3.2 - 3) / 0.3 = 0.66

Hence P(2.5 < x < 3.2) = P(-1.66 < z < 0.66) = [area to the left of z = 0.66] - [area to the left of -1.66]

= 0.7454 - 0.0485 = 0.6969

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