A population of values has a normal distribution with μ=154.6 and σ=33.9 You intend to draw a random sample of size n=86. Find the probability that a single randomly selected value is less than 145.5. P(X < 145.5) =  Round to 4 decimal places. Find the probability that the sample mean is less than 145.5. P(¯¯¯XX¯ < 145.5) =  Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.   A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 228.1-cm and a standard deviation of 1.2-cm. For shipment, 16 steel rods are bundled together. Find the probability that the average length of rods in a randomly selected bundle of steel rods is greater than 227.1-cm. P(¯¯¯XX¯ > 227.1-cm) =  Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

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