Question

Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is
approximately normal with mean 100 years and standard deviation 15 years. Based on the estimate, which
of the following is closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the
distribution?

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.

Answer 2

The closest estimate to the age of a Galápagos Islands giant tortoise at the 90th percentile of the  distribution is 119.35 years

The given parameters are:

$\mathbf{\mu = 100}$ -- population mean

$\mathbf{\sigma = 15}$ --- standard deviation

$\mathbf{p = 90\%}$ --- p-value

The z value at p-value = 90% is 1.29

So, we have:

$\mathbf{z = 1.29}$

The formula for z-value is:

$\mathbf{z = \frac{x - \mu}{\sigma}}$

So, we have:

$\mathbf{1.29 = \frac{x - 100}{15}}}$

Multiply both sides by 15

$\mathbf{19.35= x - 100}$

Add 100 to both sides

$\mathbf{x = 119.35}$

Hence, the closest estimate is 119.35 years

Read more about estimates at:

https://brainly.com/question/17810589