The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 269 days and standard deviation 19 days.Use a normal z-table to answer all questions below. If not,your answers may be marked as incorrect due to rounding issues.(a) What proportion of pregnancies last less than 270 days (about 9 months)? (Use 4 decimal places)(b) What proportion of pregnancies last between 240 and 270 days (roughly between 8 months and 9 months)? (Use 4 decimal places)(c) The longest 20% of pregnancies last days or longer. (Round to an integer.)(d) What are the quartiles of the distribution of lengths of human pregnancies? Q1 = days (Round to an integer.)Q3 = days (Round to an integer.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 269 days and standard deviation 19 days.
Use a normal z-table to answer all questions below. If not,your answers may be marked as incorrect due to rounding issues.
(a) What proportion of pregnancies last less than 270 days (about 9 months)?
(Use 4 decimal places)
(b) What proportion of pregnancies last between 240 and 270 days (roughly between 8 months and 9 months)?
(Use 4 decimal places)
(c) The longest 20% of pregnancies last days or longer. (Round to an integer.)
(d) What are the
Q3 = days (Round to an integer.)
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