Question

The average length of a human pregnancy is normally distributed, having a mean duration until birth (μ) of 266 days and a standard deviation (σ) of 16 days.

What percentage of pregnancies will last between 246 and 290 days?

What percentage of pregnancies will last less than 290 days?

Answer 1

solution

given that

mean =   = 266

standard deviation = = 16  

P(246< x < 290) = P[(246- 266) / 16< (x - ) / < (290- 266) /16 )]

= P(-1.25 < Z <1.5 )

= P(Z <1.5 ) - P(Z <-1.25 )

Using z table   

= 0.9332-0.1056

=0.8276

answer=82.76%

(B)P(X< 290) = P[(X- ) / < (290-266) / 16]

= P(z <1.5 )

Using z table

=0.9332

answer=93.32%