To find the probability that the number of correct answers is fewer than 4, we need to calculate the cumulative probability up to 3 correct answers. Since each trial has a probability of success (correct) given by p = 0.45, we can use the binomial distribution formula to calculate the probabilities.
The formula for the binomial distribution is:
P(x) = (n C x) * (p^x) * ((1 - p)^(n - x))
Where:
P(x) is the probability of getting x successes,
n is the number of trials,
x is the number of successes,
p is the probability of success in a single trial, and
(1 - p) is the probability of failure in a single trial.
Now, let's calculate the probability that the number of correct answers is fewer than 4:
P(x < 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)
P(x < 4) = (7 C 0) * (0.45^0) * (0.55^7) + (7 C 1) * (0.45^1) * (0.55^6) + (7 C 2) * (0.45^2) * (0.55^5) + (7 C 3) * (0.45^3) * (0.55^4)
You can use these calculations to find the numerical value of P(x < 4).