part of an X-ray imaging machine follows a normal distribution with a mean of 6.75 years and a standard deviation of 1.6 years. a. Calculate the probability that a randomly-selected X-ray tube will have a lifespan of:

Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Find the 87th percentile.

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z < c) = 0.738 , how do you find c?

Suppose, household color TVs are replaced at an average age of μ = 9.0 years after purchase, and the (95% of data) range was from 5.8 to 12.2 years. Thus, the range was 12.2 − 5.8 = 6.4 years. Let x be the age (in years) at which a color TV is replaced. Assume that x has a distribution that is approximately normal. (a) The empirical rule indicates that for a symmetric and bell-shaped distribution, approximately 95% of the data lies within two standard deviations of the mean. Therefore, a 95% range of data values extending from μ − 2σ to μ + 2σ is often used for "commonly occurring" data values. Note that the interval from μ − 2σ to μ + 2σ is 4σ in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values. Estimating the standard deviationFor a symmetric, bell-shaped distribution, standard deviation ≈ range 4 ≈ high value − low value 4 where it is estimated that about 95% of the commonly occurring data…