Question

The scores on a lab test are normally distributed with mean of 200. If the standard deviation is 20, find:

a) The score that is 2 standard deviations below the mean


b) The percentage of scores that fall between 180 and 240

c) The percentage of scores above 240

d) The percentage of scores between 200 and 260

e) The percentage of scores below 140

Answer 1

a)

score that is 2 standard deviations below the mean =mean -2*std deviation =200-2*20 =160

b)

for normal distribution z score =(X-μ)/σx

probability =P(180<X<240)=P((180-200)/20)<Z<(240-200)/20)=P(-1<Z<2)=0.9772-0.1587=0.8185~ 81.85%

c)

probability =P(X>240)=P(Z>(240-200)/20)=P(Z>2)=1-P(Z<2)=1-0.9772=0.0228~ 2.28 %

d)

probability =P(200<X<260)=P((200-200)/20)<Z<(260-200)/20)=P(0<Z<3)=0.9987-0.5=0.4987 ~ 49.87 %

e)

probability =P(X<140)=(Z<(140-200)/20)=P(Z<-3)=0.0013 ~ 0.13 %