In a local university, 10% of the students live in the dormitories. A random sample of 100 students is selected for a particular study. Carry answer to the nearest ten-thousandths. (Bonus Question) a. What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178?
b. What is the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025?

a

b

Step-by-step explanation:

From the question we are told that

   The  population proportion is  

    The sample size is  

Generally the standard error is mathematically represented as

=>  

=>  

The sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178

  Generally  

From the z-table  

the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025 is mathematically evaluated as

From the z-table  

Thus

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²