Suppose 52% of students support the idea of paying student government officers. A random sample of 400 students is taken. What is the probability that fewer than 50% of the students surveyed will express support for paying student government officers?

Answer: The probability that fewer than 50% of the students surveyed will express support for paying student government officers is 8.501 * 10^-65

Explanation:

Since fifty two percent (52%) of the surveyed students support the idea of paying student government officers, it consequently means that 48% (100% - 52%) of students are against the idea or not in support of it.

To find the probability that less than or fewer than fifty percent (< 50%) of the 400 surveyed students are in support, we must obtain the actual number of students that represent 50% of the individuals surveyed.

= (50/100) * 400

= 200 students.

Therefore, we are to find the probability that less than 200 of the surveyed students are in support of the payment. This means that at least, 201 of the surveyed students are not in support of the payment.

Since, 48/100 generally represents the percentage of students that are not in support of the idea, then we multiply 48/100 by itself up to 201 times. The opinions of the other 199 surveyed students doesn't matter

= (48/100) ^201

= 8.501 * 10^-65