Question

X 7.3.46-T Question Help If a random sample of 100 items is taken from a population in which the proportion of items having a desired attribute is p=0.35, what is the probability that the proportion of successes in the sample will be less than or equal to 0.427 The probability will be (Round to four decimal places as needed.)

Answer 1

solution:

the given information as follows:

sample size = n = 100

sample proportion or probability of success = p = 0.35

since np = 100*0.35 = 35 and n(1-p) = 100*(1-0.35) = 65 are greater than 10 so we can use the normal distribution

so mean = $\mu_{\bar p}$ = p = 0.35

SD =

p(1-p) 0p 0.35(1 – 0.35) 100 = 0.0477 n

we have to find the probability of success is less than or equal to 0.42 = $P(\bar p < 0.42)$

so corresponding z score

$z=\frac{\bar p-\mu_{\bar p}}{\sigma_{\bar p}}=\frac{0.42-0.35}{0.0477}=1.47$

$P(\bar p < 0.42)$ = value of z to the left of 1.47 from the z table = 0.9292

so, the probability will be 0.9292