1. The lengths of pregnancies in a small rural village arenormally distributed with a mean of 263 days and a standarddeviation of 13 days.

In what range would you expect to find the middle 98% of mostpregnancies? Between ___ and _____

If you were to draw samples of size 38 from this population, inwhat range would you expect to find the middle 98% of most averagesfor the lengths of pregnancies in the sample?

Between ___ and _____

2. Engineers must consider the breadths of male heads whendesigning helmets. The company researchers have determined that thepopulation of potential clientele have head breadths that arenormally distributed with a mean of 6.2-in and a standard deviationof 0.9-in.

In what range would you expect to find the middle 98% of mosthead breadths?
Between __ and ____

If you were to draw samples of size 38 from this population, inwhat range would you expect to find the middle 98% of most averagesfor the breadths of male heads in the sample?

3. The lengths of pregnancies in a small rural village arenormally distributed with a mean of 265.3 days and a standarddeviation of 12.7 days.

In what range would you expect to find the middle 50% of mostpregnancies? Between ___ and _____

4. A population of values has a normal distribution withμ=213.5μ=213.5 and σ=36.5σ=36.5. You intend to draw a random sampleof size n=138n=138.

Find the probability that a single randomly selected value isgreater than 211.
P(X > 211)

Find the probability that a sample of size n=138n=138 israndomly selected with a mean greater than 211.
P(M > 211)