Answer:
a) 0.0801
b) 0.1910
Step-by-step explanation:
a) probability of the event that numbers start with the digit 1 =P(1.5<X<2) =(2-1.5)/(4.8-1.5)=0.1515
Here mean =np =500*0.1515 =75.76
std deviation =(np(1-p))1/2 =8.02)
probability of the event that less than 65 of the numbers start with the digit 1=P(X<65)=P(Z<(64.5-75.76)/8.02)
=P(Z<-1.4041)=0.0801
b) probability of the event of the numbers start with the digit 3 =P(3<X<4) =(4-3)/(4.8-1.5)=0.3030
Here mean =np =500*0.3030 =151.52
std deviation =(np(1-p))1/2 =10.28
probability of the event that more than 160 of the numbers start with the digit 3=P(X>160)
=1-P(Z<(160.5-151.52)/10.28)=1-P(Z<0.8743)=1-0.8090 =0.1910
