Consider the value of $t$ such that 0.05 of the area under the curve is to the right of $t$. Step 1 of 2: Select the graph which best represents the given description of $t$. Answer (9) 2023 Hawkes Learning

Step 1 ：Consider the value of $t$ such that 0.05 of the area under the curve is to the right of $t$. This is a problem related to the properties of a normal distribution. In a normal distribution, the area under the curve represents the probability of an event occurring. So, the question is essentially asking for the value of $t$ that corresponds to a probability of 0.05.

Step 2 ：To solve this problem, we can use the inverse of the cumulative distribution function (CDF) of a standard normal distribution, also known as the quantile function or the percent-point function. The CDF of a standard normal distribution gives the probability that a random variable X is less than or equal to a certain value x. The inverse of the CDF, therefore, gives the value x that corresponds to a certain probability.

Step 3 ：Let's denote the probability as $p$ and set it equal to 0.05. Then, we can calculate the corresponding value of $t$ using the inverse of the CDF. The calculation gives $t$ approximately equal to 1.6448536269514722.

Step 4 ：Final Answer: The value of $t$ such that 0.05 of the area under the curve is to the right of $t$ is approximately \(\boxed{1.645}\).