The diameters of so-called "Gaussian" spheres are normally distributed with a mean of 9.35 cm and a standard deviation of 1.96 cm. By randomly selecting 64 spheres, a standard deviation of 1 cm was found. Answer the following: What is the probability that these "Gaussian" spheres have an average diameter less than 8.70 cm?
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Step 1
70 cm using the formula z = (x̄ - μ) / (σ / √n), where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Given: x̄ = 8.70 cm μ = 9.35 cm σ = 1.96 cm n = 64 Calculate z-score: z = (8.70 - 9.35) / Show more…
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