Question

test scores in a MATH 1030 class is approximately normally distributed with mean 86 and standard deviation 6. Round answers to the nearest tenth of a percent. a) What percentage of scores will be less than 88? % b) What percentage of scores will be more than 82? % c) What percentage of scores will be between 81 and 87? %

Answer 1

Solution :

(a)

P(x < 88) = P[(x - ) / < (88 - 86) / 6]

= P(z < 0.33)

= 0.6293

= 62.93%

(b)

P(x > 82) = 1 - P(x < 82)

= 1 - P[(x - ) / < (82 - 86) / 6]  

= 1 - P(z < -0.67)

= 0.2514

= 24.14%

(c)

P(81 < x < 87) = P[(81 - 86)/ 6) < (x - ) /  < (87 - 86) / 6) ]

= P(-0.83 < z < 0.17)

= P(z < 0.17) - P(z < -0.83)

= 0.3642

= 36.42%