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
mean =np
= 500 * 0.1515
= 75.76
std deviation =√(np (1 - p)) = 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)) =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
