According to a study, the length of pregnancy of a randomly selected female has a normal distribution with a mean of 272 days and a standard deviation of 15.4 days. Let X be the length of pregnancy for a randomly selected female and let X¯ be the average length of pregnancy for a random sample of size 37.
1. Describe the probability distribution of X and state its parameters μ and σ:
X∼ Select an answer unknown F B χ² T N ( μ= , σ= )
and find the probability that the length of pregnancy for a randomly selected female is less than 300 days.
(Round the answer to 4 decimal places)
2. Use the Central Limit Theorem
Select an answer the sample size is small (n<30) and the distribution of the original population is unknown the distribution of the original population is unknown the original population is normally distributed the sample size is large (n>30) although the distribution of the original population is unknown
to describe the probability distribution of X¯ and state its parameters μX¯ and σX¯: (Round the answers to 1 decimal place)
X¯∼ Select an answer N unknown T F χ² B ( μX¯= , σX¯= )
and find the probability that the average length of pregnancy for a sample of 37 randomly selected females is between 269 and 270 days.
(Round the answer to 4 decimal places)