Question

ANSWER IF YOU HAVE SOLUTION OR ELSE YOU WILL BE REPORTED!

Answer 1

Answer:

c) 0.5284

Step-by-step explanation:

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by the formula:

$z=\frac{p_s-p}{\sigma_p} \\\\where\ p_s=sample\ proportion,p=population\ proportion,\\\sigma_p=standard \ error=\sqrt{ \frac{p(1-p)}{n}},n=sample\ size\\\\ z=\frac{p_s-p}{\sqrt{ \frac{p(1-p)}{n}}} \\\\Given \ that\ n=50,p=40\%=0.4\\\\For\ p_s=0.35:\\\\z=\frac{0.35-0.4}{\sqrt{\frac{0.4(1-0.4)}{50} } } =-0.72\\\\For\ p_s=0.45:\\\\z=\frac{0.45-0.4}{\sqrt{\frac{0.4(1-0.4)}{50} } } =0.72$

Hence from the normal distribution table, P(0.35 < x < 0.45) = P(-0.72 < z < 0.72) = P(z < 0.72) - P(z < -0.72) = 0.7642 - 0.2358 = 0.5284