Final answer:
The probability that in a sample of 60 the proportion of successes exceeds 0.35 in a binomial experiment with p = 0.4 is practically zero.
Step-by-step explanation:
To find the probability that in a sample of 60 the proportion of successes exceeds 0.35 in a binomial experiment with p = 0.4, we can use the normal approximation to the binomial distribution.
First, we calculate the mean and standard deviation of the binomial distribution using np = (60)(0.4) = 24 and sqrt(np(1-p)) = sqrt((60)(0.4)(0.6)) = 3.464.
Then, we convert the problem into a z-score by finding (0.35 - 24) / 3.464 = -5.523.
Finally, we use a standard normal distribution table or a calculator to find the probability associated with a z-score of -5.523, which is essentially zero.
Therefore, the probability that in a sample of 60 the proportion of successes exceeds 0.35 is extremely small, practically zero.