求教及步驟 thx\r\n\r\n Question is:\r\n\r\n The general manager of a digital products manufacturer believes that 65% of all potential customers prefer to buy MP3 players with over 8GB built-in memory. A random sample of 100 customers was chosen.\r\n\r\n\r\na . If the general manager's brlief is true , what is the mean and the standard deviation of the sample proportion of customers who prefer to buy MP3 players with over 8GB built-in memory?\r\n\r\n\r\nb. If the general manager's belief is true , what is the probability that the sample proportion of customers who prefer to buy MP3 players with over 8GB built - in memory is less than 0.75 ?\r\n\r\n\r\nthx
(a) The mean of the sample proportion
= the mean of the population proportion
= 65%
The standard deviation of the sample proportion
= √[(65%)(35%)/100]
= 4.77%
(b) Pr(p < 0.75)
= Pr[z < (0.75 - 0.65)/0.0477]
= Pr(z < 2.097)
= 0.9820