A statistics class has a population of 140 students of which 55% are female. A random sample of 40 students was selected. What is the probability that 24 or more from this sample will be female?

The probability that 24 or more from this sample will be female is 0.2643.

Step-by-step explanation:

Define X as the number of female students.

The random variable X follows a Binomial distribution with parameters n = 40 and p = 0.55.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

1.np ≥ 10

2.n(1 - p) ≥ 10

Check the conditions as follows:

Thus, a Normal approximation to binomial can be applied.

So,  X follows normal distribution with mean and standard deviation:

Compute the probability that 24 or more from this sample will be female as follows:

Thus, the probability that 24 or more from this sample will be female is 0.2643.

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