Question

The lengths of pregnancies in a small rural village are normally distributed with a mean of 262 days and a standard deviation of 12 days. In what range would you expect to find the middle 68% of most pregnancies? Between ----and ---- If you were to draw samples of size 48 from this population, in what range would you expect to find the middle 68% of most averages for the lengths of pregnancies in the sample? Between ----and ------ Enter your answers as numbers. Your answers should be accurate to 1 decimal places.

Answer 1

Solution :

Given that,

= 262

= 12

n = 48

= 262

= / n = 12 / 48

Using Empirical rule,

1)

P( - 1< X < + 1) = 68%

P(262 - 12 < X < 262 + 12) = 68%

P(250< X < 274) = 68%

Range is : 250 to 274

2)

P(  - 1 < X <   + 1 ) = 68%

P(262 - 12 / 48 < < 262 + 12 / 48) = 68%

P(260.3 < < 263.7) = 68%

Range is : 260.3 to 263.7