Question

The lifespans of tigers in a particular zoo are normally distributed. The average tiger lives 22.4 22.422, point, 4 years; the standard deviation is 2.7 2.72, point, 7 years. Use the empirical rule ( 68 − 95 − 99.7 % ) (68−95−99.7%)left parenthesis, 68, minus, 95, minus, 99, point, 7, percent, right parenthesis to estimate the probability of a tiger living longer than 14.3 14.314, point, 3 years. HELP

Answer 1

Answer: .15%

Explanation:

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Answer 2

To estimate the probability of a tiger living longer than 14.3 years, we will use the empirical rule, which states that for a normal distribution:

68% of data falls within one standard deviation of the mean

95% of data falls within two standard deviations of the mean

99.7% of data falls within three standard deviations of the mean

First, we need to convert the given value of 14.3 years into standard units. We can do this by using the following formula:

Z = (x - mean) / standard deviation

where x is the value in question (14.3 years), mean is the average lifespan of a tiger (22.4 years), and standard deviation is the standard deviation of tiger lifespans (2.7 years).

Z = (14.3 - 22.4) / 2.7 = -4.1

This means that a tiger living for 14.3 years is 4.1 standard deviations below the mean.

Since we know that 99.7% of data falls within three standard deviations of the mean, we can conclude that the probability of a tiger living longer than 14.3 years is less than 0.3% (or 0.003). Therefore, it is very unlikely that a tiger in this zoo will live longer than 14.3 years.

Uday Tahlan