Question

The lengths of pregnancies in a small rural village are normally distributed with a mean of 260 days and a standard deviation of 12 days. A distribution of values is normal with a mean of 260 and a standard deviation of 12.

What percentage of pregnancies last beyond 264 days?
P(X > 264 days) = Incorrect %

Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Solution :

Given, X follows Normal distribution with,

   = 260

   = 12  

Find P(X > 264)

= P[(X - )/ >  (264 - )/]

= P[Z > (264 - 260)/12]

= P[Z > 0.333]

= 1 - P[Z < 0.333]

= 1 - 0.6304 ...... ( use z table)

= 0.3696 = 37.0

P(X > 264) = 37.0