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X is a random variable with a mean of 36 and a standard deviation of 10 that represents the percent of fat calories consumed by each American each day.

If a random variable X has a normal distribution with a mean of $\mathrm{μ}$and a standard deviation of s, it is denoted as $X~N(\mathrm{μ},s)$.

The random variable $X$ is denoted as $X~N(36,10)$in this case.

As a result, we infer that the random variable X representing the percent of fat calories consumed each day by an American is denoted as $X~N(36,10)$.

X is a random variable that represents the percent of fat calories consumed each day by an American, such that$X~N(36,10)$.

This indicates a $\mathrm{μ}=36$ mean and a$s=10$ standard deviation.

The probability that the percent of fat calories that a person in America consumes each day is more than 40 is given as:

$\begin{array}{rcl}P(x& >& 40)=P\left(\frac{x-\mathrm{μ}}{\mathrm{σ}}>\frac{40-36}{10}\right)\\ & =& P(z>0.4)\end{array}$

The required probability is shown by the shaded region in the graph below. Hence, it can be written as:

$P(z>0.4)=0.5-P(0≤z≤0.4)$$=0.5$

Therefore, we conclude that the probability that percent of fat calories that a person in America consumes each day is more than 40 is given by $P(x>40)=\mathbf{0}\mathbf{.}\mathbf{3446}$

X is a random variable denoting the percent of fat calories that a person in America consumes each day, such that $X~N(36,10)$.

This implies, Mean, $\mathrm{μ}=36$ and standard deviation, $s=10$.

The probability that the percent of fat calories for an individual is less than k is given by:

$P(x<k)=P\left(\frac{x-\mathrm{μ}}{\mathrm{σ}}<\frac{k-36}{10}\right)=P\left(z<z_1\right)=0.25$

From the normal distribution tables, we get

Replacing x with k and z with$z_1$in the equation, $x=\mathrm{μ}+z\mathrm{σ}$, we get

The required probability is shown by the shaded region in the graph below.

Therefore, we conclude that the maximum number for the lower quarter of percent of fat calories $(X)$ that a person in America consumes each day is $\mathbf{29}\mathbf{.}\mathbf{26}$