3. Female Beluga whales weigh 850 kg on average, with a standard deviation of 80

Question

3. Female Beluga whales weigh 850 kg on average, with a standard deviation of 80 kg. Male Beluga whales weigh 900 kg on average with a standard deviation of 100 kg. If two independent random samples of size 12 and 16 are taken from females and males, respectively, and the sample variances, sF^2 and sM^2, are calculated, what is the probability that:

a. The ratio of the variance of female weights to that of males is less than 0.235 (i.e., sF^2/sM^2 < 0.235) b. The ratio of the variance of female weights to that of males is more than 1.32.

Explanation / Answer

3. Female Beluga whales weigh 850 kg on average, with a standard deviation of 80 kg. Male Beluga whales weigh 900 kg on average with a standard deviation of 100 kg. If two independent random samples of size 12 and 16 are taken from females and males, respectively, and the sample variances, sF^2 and sM^2, are calculated, what is the probability that:

a. The ratio of the variance of female weights to that of males is less than 0.235 (i.e., sF^2/sM^2 < 0.235)

Df1=12-1=11

Df2=16-1=15

P( F <0.235) = 0.00995

=0.0100

b. The ratio of the variance of female weights to that of males is more than 1.32.

P( F > 1.32) = 0.3026

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