Answer:
2.5% probability of a lion living less than 7.2 years
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 10
Standard deviation = 1.4
Probability of a lion living less than 7.2 years
The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.
7.2 = 10 - 2*1.4
So 7.2 is two standard deviations below the mean.
By the empirical rule, of those 50% of the measures below the mean, 95% is within 2 standard deviations of the mean, that is, between 7.2 and 10, and 5% are less than 7.2. So
p = 0.05*0.5 = 0.025
2.5% probability of a lion living less than 7.2 years
