Assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are $n=8$ trials, each with probability of success (correct) given by $p=0.6$. Find the indicated probability for the number of correct answers.
Find the probability that the number $x$ of correct answers is fewer than 4 .
\[
P(X< 4)=
\]
(Round to four decimal places as needed.)

Step 1 ：Assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are $n=8$ trials, each with probability of success (correct) given by $p=0.6$.

Step 2 ：We need to find the probability that the number $x$ of correct answers is fewer than 4.

Step 3 ：We can use the binomial probability formula to calculate this probability.

Step 4 ：The binomial probability formula is given by $P(X=k) = C(n, k) * p^k * (1-p)^{n-k}$, where $C(n, k)$ is the number of combinations of $n$ items taken $k$ at a time, $p$ is the probability of success, and $k$ is the number of successes.

Step 5 ：We calculate $P(X<4)$ by summing up the probabilities $P(X=k)$ for $k=0,1,2,3$.

Step 6 ：Using the binomial probability formula, we find that $P(X<4) = \sum_{k=0}^{3} C(8, k) * 0.6^k * (1-0.6)^{8-k}$.

Step 7 ：Calculating this sum, we find that $P(X<4) \approx 0.1736704$.

Step 8 ：Thus, the probability that the number $x$ of correct answers is fewer than 4 is approximately \(\boxed{0.1737}\).