Question

Stat 5.2.18-1 Question Help ced Test Composte Use the normal distribution to the right to answer the questions (a) What percent of the scores are less than 197 (b) Out of 1500 randomly selected scores, about how many would be expected to be greater than 21? Home 20.1 0 aments Plan % ebook (a) The percent of scores that are less than 19 is (Round to two decimal places as needed) Crunch apter Content scessible Resol kills for success er thenswer box and then click Check Answer Tools for succord LATITUDE E6410

Answer 1

a) P ( X<19 )=P ( X−μ<19−20.1 )=P ((X−μ)/σ<(19−20.1)/5.6)
Since (x−μ)/σ=Z and (19−20.1)/5.6=−0.2 we have:
P (X<19)=P (Z<−0.2)
Use the standard normal table to conclude that:
P (Z<−0.2)=0.4207= 42.07%

b) n=1500

o(T) = 5.6/ (1500) = 5.6/38.73 = 0.14

P ( X>21 )=P ( X−μ>21−20.1 )=P ((X−μ)/σ>(21−20.1)/0.14)
Since Z=(x−μ)/σ and (21−20.1)/0.14=6.43 we have:
P ( X>21 )=P ( Z>6.43 )
Use the standard normal table to conclude that:
P (Z>6.43)=0