Question

.

Answer 1

Solution:

Given that,

p = 30% = 0.30

1 - p = 1 - 0.30 = 0.70

n = 6500

Here, BIN (6500 , 0.30)

According to normal approximation binomial,

X Normal

Mean = = n*p = 6500 * 0.30 = 1950

Standard deviation = =n*p*(1-p) = [6500*0.30*0.70]  = 36.9459064038

Now ,

P(1920< x< 1994)

= P(X < 1994) - P(X < 1920)

=  P[(X - )/ <  (1994- 1950)/36.9459064038] -   P[(X - )/ <  (1920- 1950)/36.9459064038]

= P[Z < 1.19] - P[Z < -0.81]

= 0.8830 - 0.2090 ..Use z table

= 0.6740

= 0.67

Answer : 0.67 (in percentage 67.40% )