Question

Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is

Answer 1

Answer:

The 90th percentile for the life span of the Galápagos Islands giant tortoise is 119.4 years.

Step-by-step explanation:

Let X denote the  life span of the Galápagos Islands giant tortoise.

It is provided that x follows a normal distribution with mean 100 years and standard deviation 15 years.

Compute the 90th percentile value as follows:

P (X < x) = 0.90

⇒ P (Z < z) = 0.90

The corresponding value of z is, z = 1.29.

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma}\\\\1.29=\frac{x-100}{15}\\\\x=100+(1.29\times 15}\\\\x=119.35\\\\x\approx 119.4$

Thus, the 90th percentile for the life span of the Galápagos Islands giant tortoise is 119.4 years.