2 The adult male striped skunk population in southern California has the followi

Question

2 The adult male striped skunk population in southern California has the following population parameters for skull width: = 53 mm: = 7.5 mm. Assuming that skull widths are normally distributed, what proportion of the population have skull widths a. Less than 58 mm? (1 point) b. Equal to 50 mm? (1 point) 3· The female skunks of this same population have a mean skull width of = 49 mm ( = 6.5 mm). a. What proportion of the population should have skull widths between 48 and 52mm? 1 point) b. What proportion of females in a sample of 7 should be greater than (or equal to) the mean of the male skulls? (1 point)

Explanation / Answer

Answers below:

2.

a. P(X<58) = P(Z< 58-53 / 7.5)
= P(Z< .67)
= .7486

b. P(X=50) = P(Z = 50-53/7.5) = P(Z = -.4) = .3446

3.

a. Mean = 49

Stdev = 6.5

a. P(48<Z<52) = P(48-49 / 6.5<Z< 52-49/6.5) = P(-.154<Z<.462) = .68-.44 = .24

b. P(X>53) = P(t> 53-49 / (6.5/sqrt(7)) = P(t>1.63) = .77112

We have used t distribution in this case because n<30

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