Question

If I am sampling from a Population that has P=.6 and my sample size is 400. Find the following probabilities. 3 points each, 3 decimal places

A. P(pത < .56) = __________

B. P(pത > .63) = _____________

C. P(.58 < pത < .62) = _____________

Answer 1

GIVEN:

Population proportion

Sample size

FORMULA USED:

We convert the sample proportion into the standard score to calculate the probability. The formula for standard score is given by,

CALCULATION:

(A) PROBABILITY THAT SAMPLE PROPORTION IS LESS THAN 0.56 :

The probability that the sample proportion is less than 0.56 is,

  

  

  

Using the z table, the probability value is the value with corresponding row -1.6 and column 0.03.

Thus the probability that the sample proportion is less than 0.56 is .

(B) PROBABILITY THAT SAMPLE PROPORTION IS MORE THAN 0.56 :

The probability that the sample proportion is more than 0.63 is,

  

  

  

   {Since }

Using the z table, the probability value is the value with corresponding row 1.2 and column 0.02.

Thus the probability that the sample proportion is more than 0.63 is .

(C) PROBABILITY THAT SAMPLE PROPORTION LIES BETWEEN 0.58 AND 0.62 :

The probability that the sample proportion lies between 0.58 and 0.62 is,

  

  

  

   {Since }

Using the z table, the first probability value is the value with corresponding row 0.8 and column 0.02 and the second probability value is the value with corresponding row -0.8 and column 0.02

Thus the probability that the sample proportion lies between 0.58 and 0.62 is .