Question

One of the most common problems Statistics students have when studying the Normal Distribution is distinguishing between two question types refered to by the author of your text as

?"Finding the probability of a normal random? variable" and? "Finding the value of a normal random? variable." ? (See section? 7.2) One of each is shown below. Identify which is which and give the answer to the question.

Lengths of pregnancy for women who go into spontaneous labor is normally distributed with mean of 270 days and standard deviation of 9 days.

? (a) If? 60% of women have a pregnancy length below this number of? days, what is the number of? days?

?(b) What percentage of women who go into spontaneous labor have a pregnancy that lasts

279 days or? fewer?

Answer 1

Solution:-

Given that,

mean = = 270 days.

standard deviation = = 9 days

a) Using standard normal table,

P(Z < z) = 60%

= P(Z < z) = 0.60  

= P(Z < 0.25) = 0.60

z = 0.25

Using z-score formula,

x = z * +

x = 0.25 * 9 + 270

x = 272.25

x = 272 days

b) P(x < 279) = P[(x - ) / < (279 - 270) / 9]

= P(z < 1.00 )

Using z table,

= 0.8413

The percentage is = 84.13%