The length of human pregnancies from conception to birth varies according to a d

Question

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 259 days and standard deviation 16 days. What proportion of pregnancies last less than 270 days (about 9 months)? (Please use 4 decimal places.) What proportion of pregnancies last between 240 and 270 days (roughly between 8 months and 9 months)? (Please use 4 decimal places.) How long do the longest 20% of pregnancies last? (Please use 2 decimal places.) The quartiles of any distribution are the values with cumulative proportions 0.25 and 0.75. What are the quartiles of the standard Normal distribution? (Use 2 decimal places.) Q1 = Q3 = What are the quartiles of the distribution of lengths of human pregnancies? Please use 2 decimal places. Q1 = Q3 =

Explanation / Answer

mean = 259

standard deviation = 16

a)z value of 270 is (270-259)/16 = 0.6875,p value = 0.754116

P(pregrencies last less than 270 days) = 0.75

b)z value of 240 is (240-259)/16 = -1.1875,p value =0.117

P(pregrencies last less than 240 days) =0.117

P(pregrencies last between 240 and 270 days) = 0.75-0.117 = 0.633

c)let the longest 20% last l days

P(X<l) = 0.8

z value for p=0.8 is 0.841

(l-259)/16 = 0.841

l - 259 = 16*0.841 => l = 259+16*0.841 => l = 272.456

longest 20% last 272 days

d)standard normal distribution has mean = 0 and standard deviation =1

z vlaues for p=0.25 and p=0.75 are -0.67449 and 0.67449

(Q1-0)/1 = -0.67449

Q1 = -0.67

Q3 = 0.67

e)(Q1-259)/16 = -0.67449

Q1 = 259 - 0.67449*16 = 248.208 = 248.21

(Q3-259)/16 = 0.67449

Q3 = 259 + 0.67449*16 = 269.79

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