Question

The mean incubation time for a type of fertilized egg kept at

100.31?°F is 21 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 2 days

?(a) What is the probability that a randomly selected fertilized egg hatches in less than 19 days??(b) What is the probability that a randomly selected fertilized egg hatches between 17 and 21days? ?(c) What is the probability that a randomly selected fertilized egg takes over 23 days to? hatch?

?(a) The probability that a randomly selected fertilized egg hatches in less than 19 days is nothing .

?(Round to four decimal places as? needed.)

Answer 1

Solution :

Given that ,

mean = = 21

standard deviation = = 2

P(x < 19) = P((x - ) / < (19 - 21) / 2) = P(z < -1)

Using standard normal table,

P(x < 19) = 0.1587

Probability = 0.1587

(b)

P( 17 < x < 21) = P((17 - 21 / 2) < (x - ) / < (21 - 21) / 2) )

P( 17 < x < 21) = P(-2 < z < 0)

P( 17 < x < 21) = P(z < 0) - P(z < -2) = 0.5 - 0.0228

Probability = 0.4772

(c)

P(X > 23) = 1 - P(x < 23)

= 1 - P((x - ) / < (23 - 21) / 2)

= 1 - P(z < 1)   Using standard normal table,

= 1 - 0.8413

= 0.1587

P(x > 23) = 0.1587

Probability = 0.1587