In a normal distribution, if mean is 8 and standard deviation is 1.5, how many percent of data fall

Question

Show the complete solution: In a normal distribution, if mean is 8 and standard deviation is 1.5, how many percent of data fall

a.     Above 8.5?

b.     Between 7.2 and 8.5?

Answer 1

x = data value N(8,1.5)

want to find P(x > 8.5)

translate inequality to N(0,1)

P(x > 8.5) = P(z > (8.5-8)/1.5) = P(z > 0.333) = P(z < -0.333) (look up in table or use technology)

P(7.2 < x < 8.5)

translate inequality to N(0,1)

P(7.2 < x < 8.5) = P( (7.2-8)/1.5 < z < (8.5 - 8)/1.5) = P(-0.533 < z < 0.333) = P(z < 0.333) - P(z < -0.533) (look up in table or use technology)

Answer 2

find the z score = (x - x bar)/sd = (8.5-8)/1.5 = .5/1.5 = 1/3 = about .3333

use z tables or a z calculator

P(x>8.5) = .36945 = about 37% fall larger than 8.5

for P(7.2 < x < 8.5) find the z score for 7.2

(7.2-8)/1.5= -.8/1.5 = -.8(2/3) =-1.6/3 = -.5333

then use a z calculator or z tables to find the % for between 7.2 an 8

then add that to % between 8 and 8.5 to get about 37% + 20% = 57%