Question

The lengths of a particular animal's pregnancies are approximately normally distributed, with mean μ equals=271

days and standard deviation σ equals=20days.

(a) What proportion of pregnancies lasts more than 286 days?

(Round to four decimal places as needed.)

(b) What proportion of pregnancies lasts between 256 and 281 days?

(Round to four decimal places as needed.)

(c) What is the probability that a randomly selected pregnancy lasts no more than 266 days?

(Round to four decimal places as needed.)

(d) A "very preterm" baby is one whose gestation period is less than 226 days. Are very preterm babies unusual?

(Round to four decimal places as needed.)

The probability of this event is _____ so it _____ be unusual because the probability is _______ than 0.05.

(Round to four decimal places as needed.)

Answer 1

Solution :

Given that ,

mean = = 271

standard deviation = = 20

(a)

P(x > 286) = 1 - P(x < 286)

= 1 - P((x - ) / < (286 - 271) / 20)

= 1 - P(z < 0.75)

= 1 - 0.7734

= 0.2266

P(x > 286) = 0.2266

Proportion = 0.2266

(b)

P(256 < x < 281) = P((256 - 271)/ 20) < (x - ) / < (281 - 271) / 20) )

= P(-0.75 < z < -0.50)

= P(z < -0.50) - P(z < -0.75)

= 0.3085 - 0.2266

= 0.0819

Proportion = 0.0819

(c)

P(x 266) = P((x - ) / (266 - 271) / 20)

= P(z -0.25)

Using standard normal table,

P(x ) = 0.4013

Proportion = 0.4013

(d)

P(x < 226) = P((x - ) / < (226 - 271) / 20)

= P(z < -2.25)

P(x < 226 ) = 0.0122

0.0122 < 0.05

The probability of this event is 0.0122 so it can be unusual because the probability is less than 0.05