Question

The area under a density curve that lies to the left of 60 is $0.364$. What percentage of all possible observations of the variable are

a. Less than 60?

b. At least 60?

Short answer

a. The percentage of all observations of the variable is $=36.4\%$.

b. The percentage of all observations of the variable is$=63.6\%$.

Step-by-step solution

Part (a) Step 1: Given Information 

The area under a density curve that lies to the left . The percentage of all possible observations of the variable are less than 60 .

Part (a) Step 2: Explanation

The percentage of all possible observations of the variable that fall inside the specified range, represented as a percentage of the corresponding area under the curve.

The variable has a percentage of all possible observations of less than $60$.

$=0.364\times 100$

$=36.4\%$

Hence, the percentage of all observations of the variable is $=36.4\%$.

Part (b) Step 1: Given Information 

The area under a density curve that lies to the left. The percentage of all possible observations of the variable are at least 60 .

Part (b) Step 2: Explanation 

The percentage of all possible observations of the variable that fall inside the specified range, represented as a percentage of the corresponding area under the curve.

The probability of at least $60$potential observations of the variable is

$=1-0.364$

$=0.636$

Calculate the probability percentages.

$=0.636\times 100$

$=63.6\%$

Hence, the percentage of all observations of the variable is $63.6\%$.$=63.6\%$