scientists estimate that the distribution of the life - span of the galápagos islands giant tortoise is…

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?\na 80 years\nb 115 years\nc 120 years\nd 125 years\ne 130 years

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?\na 80 years\nb 115 years\nc 120 years\nd 125 years\ne 130 years

Answer

Explanation:

Step1: Find the z - score for 90th percentile

Looking up in the standard normal distribution table (z - table), the z - score corresponding to a cumulative probability of 0.90 is approximately $z = 1.28$.

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the original normal distribution, $\mu$ is the mean, and $\sigma$ is the standard deviation. We know $\mu = 100$, $\sigma=15$ and $z = 1.28$. Rearranging the formula for $x$ gives $x=\mu+z\sigma$.

Step3: Calculate the value of $x$

Substitute $\mu = 100$, $z = 1.28$ and $\sigma = 15$ into the formula $x=\mu+z\sigma$. So $x=100 + 1.28\times15=100+19.2 = 119.2\approx120$.

Answer:

C. 120 years