Question

The length of human pregnancies from conception to birth varies according to a distribution that can be modeled by a normal random variable with mean 267 days and standard deviation 15 days.

Question 1. What percent of pregnancies last less than 240 days? Note that the answer is requested as a percent. Use 2 decimal places in your answer.

%

Question 2. What percent of pregnancies last between 240 and 270 days? Note that the answer is requested as a percent. Use 2 decimal places in your answer.

%

Question 3. The longest 20% of pregnancies last at least how many days? (round to the nearest whole day)

days.

Answer 1

Solution :

Given that ,

mean = = 267

standard deviation = =15   

P(X< 240) = P[(X- ) / < (240-267) /15 ]

= P(z <-1.8 )

Using z table

= 0.0359

=3.59%

Question 2.

P(240< x < 270) = P[(240 - 267) /15 < (x - ) / < (270 - 267) / 15)]

= P( -1.8< Z < 0.2)

= P(Z < 0.2) - P(Z < -1.8)

Using z table   

= 0.5793 - 0.0359

   = 0.5434

=54.34%

Question 3.

Using standard normal table,

P(Z > z) = 20%

= 1 - P(Z < z) = 0.20

= P(Z < z ) = 1 - 0.20

= P(Z < z ) = 0.80

= P(Z < z ) = 0.80

z =0.84 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 0.84*15+267

x= 297.6

x=298 days (rounded)