Question

1. The lengths of pregnancies in a small rural village are normally distributed with a mean of 263 days and a standard deviation of 13 days.

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

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

Between ___ and _____

2. Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.2-in and a standard deviation of 0.9-in.

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

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

3. The lengths of pregnancies in a small rural village are normally distributed with a mean of 265.3 days and a standard deviation of 12.7 days.

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

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

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

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

Answer 1

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n = 138 and sigma = σ / sqrt(n) = 36.5 / sqrt(138) = 3.1072