Theprobabilitythat an item chosen at random from themanufacturer'sproductionis less than 1.6 inches long is approximately 0.0010 or 0.1%.To calculate the probability that an item chosen at random from the manufacturer's production is less than 1.6 inches long, we can use the properties of thenormal distribution.Given:Mean (μ) = 10.5 inchesStandard Deviation(σ) = 3.2 inchesTo find the probability, we need to standardize the value of 1.6 inches using the z-score formula and then look up the corresponding area under the standard normal distribution curve.Thez-score formulais:z = (x - μ) / σwhere:x = 1.6 inches (value we want to find the probability for)μ = 10.5 inches (mean)σ = 3.2 inches (standard deviation)Calculating the z-score:z = (1.6 - 10.5) / 3.2z = -9.9 / 3.2z ≈ -3.09375Now, we need to find the cumulative probability for z = -3.09375 using a standard normal distribution table or a statistical calculator. The cumulative probability represents the area under the curve to the left of the given z-score.Using a standard normal distribution table, we find that the cumulative probability for z = -3.09375 is approximately 0.0010.Therefore, the probability that an item chosen at random from the manufacturer's production is less than 1.6 inches long is approximately 0.0010 or 0.1%.To know more aboutprobabilityclick-brainly.com/question/24756209#SPJ11...

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