Suppose a simple random sample of size n = 75 is obtained from a population whos

Question

Suppose a simple random sample of size n = 75 is obtained from a population whose size is N = 30,000 and whose population proportion with a specified characteristic is p = 0.8. Complete parts (a) through (c) below Determine the mean of the sampling distribution of p. mu_p = .8 (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. sigma_p = .046188 (Round to six decimal places as needed.) What is the probability of obtaining x = 66 or more individuals with the characteristic ? That is, What is P(p Greaterthanorequalto 0.88)? P(p Greaterthanorequalto 0.88) = .0418 (Round to four decimal places as needed.) What is that probability of obtaining x = 57 or fewer individuals with the characteristic? That is, what is P(p lessthanorequalto 0.76)? P(p lessthanorequalto 0.76) = (Round to four decimal places as needed.)

Explanation / Answer

c)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.76      
u = mean =    0.8      
          
s = standard deviation =    0.046188      
          
Thus,          
          
z = (x - u) / s =    -0.866025808      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.866025808   ) =    0.193238005 [ANSWER]

************************

If you use tables, then:

Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.87   ) =    0.1922 [ALTERNATE ANSWER, USING TABLES]

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.