Question

Based on historical data, your manager believes that 33% of the company's orders come from first-time customers. A random sample of 245 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.22 and 0.39? (Enter your answer as a number accurate to 4 decimal places.)

Answer #1

Solution :

Given that ,

p = 0.33

1 - p = 0.67

n = 245

= p = 0.33

= (p*(1-p))/n = (0.33*0.67)/ 245= 0.03004

P(0.22 < < 0.39 ) = P((0.22 - 0.33)/0.03004 ) < ( - ) / < (0.39 - 0.33) /0.03004 ) )

= P(-3.662 < z < 1.997 )

= P(z < 1.997) - P(z < -3.662)

= 0.9771 - 0.0001

= 0.9770

**Probability = 0.9770**

**The probability that the sample proportion is between
0.22 and 0.39 is 0.9770.**

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