In a large university, 70% of the students live in the dormitories. A random sample of 110 students is selected for a particular study. The probability that the sample proportion of students living in the dormitories falls in between 0.6 and 0.8 equals a.0.9780 b.0.9318 c.0.9365 d.1.6450

The correct option is (a) 0.9780.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

The standard deviation of this sampling distribution of sample proportion is:

As the sample selected is quite large, i.e. n = 110 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample proportion by a Normal distribution.

The mean and standard deviation are:

Compute the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 as follows:

*Use a z-table.

Thus, the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 is approximately equal to 0.9780.

The correct option is (a).

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