# proportion and distribution

• Mar 22nd 2011, 11:15 PM
sanja85
proportion and distribution
The duration of pregnancy in humans is approximately Normally distributed with μ = 266 days and σ = 16 days. In the following questions, assume that this distribution is exact.

(a) What proportion of pregnancies last between 250 and 290 days?

(b) A post-term pregnancy is defined as one that lasts more than 294 days. What proportion of pregnancies are post-term?

(c) What durations give the quartiles of the distribution of human pregnancy durations?
• Mar 22nd 2011, 11:46 PM
Sambit
If 'X' is a random variable which denotes 'duration of pregnancy in humans', then $X\sim N(\mu=266, \sigma^2=16^2)$.

(a) Required to find $P(250

= $P(\frac{250-266}{16}<\frac{X-266}{16}<\frac{290-266}{16})$

= $P(-1 (put the values)

(b) Required to find $P(X>294)$

$=P(\frac{X-266}{16}>\frac{294-266}{16})$

= $1-\Phi(1.75)$ (put the value)

(c) Find Q's such that $P(X, $P(X while $Q_2$ is $\mu=266$

"Standardization" has been done in (a) and (b); Z is a standard normal variate and $\Phi(.)$ denotes the CDF of a standard normal distribution.
• Mar 30th 2011, 08:44 AM
sanja85
what do you mean by ("put the value")? and i don't understand (c)
• Mar 30th 2011, 03:38 PM
mr fantastic
Quote:

Originally Posted by sanja85
what do you mean by ("put the value")? and i don't understand (c)

To better understand the help you have been given, it might be best at this stage to go back and review this material in your class notes and textbook.
• Mar 31st 2011, 04:48 AM
Sambit
Quote:

Originally Posted by sanja85
what do you mean by ("put the value")? and i don't understand (c)

I mean put the values of $\Phi(1),\Phi(1.5)$ etc. these are the values of a standard normal cdf. A standard textbook should have a table containing these values in its appendix.
• Apr 3rd 2011, 09:21 AM
sanja85
1.5-1+(1) would be
0.9332-1+0.8413
which then equals
0.7745
:)