Question

The population of scores on the SAT is normally distributed with a µ = 500 and σ = 100. If you were to take a random sample of 48 students who had taken the SAT, what are the chances that their mean would be less than 520?

Answer 1

Solution: population of scores on the SAT Normally distributed with mean mu = 500 h theta = 100, if a sample of 48 students it taken then we have to find p i bar{x} < 520 p[bar{x} < 520] = p[bar{x} - 500/100/squareroot 4theta < 520 - 500/100 squareroot 4theta] = p[z < 1.3theta] = 0.5 + p[0 < z < 1.3theta] = 0.5 + 4102 p[bar{x} < 520] = 9162

Answer 2

SOLUTION :

SD of sample = SD of population / sqrt( sample size)

= 100/sqrt(48) 

= 14.4338 

P( x < 520) = P(z < (520 - 500)/14.4338) = P(z < 1.3856)

= 0.9162 + (0.9177 - 0.9162)* 56/100

= 0.9170 

= 91.70 % 

So, chances to be less than 520 score = 91.70 % (ANSWER).