Please help answer the following questions, Suppose you have a random sample of

Question

Please help answer the following questions,

Suppose you have a random sample of 300 observations whose histogram and QQ-plot both seem to indicate that the data is approximately normal. If you wanted to get a quick estimate of the standard deviation based on the range of the data, how many standard deviations would approximately equal the range? (Use a whole number - this is just an estimate.)

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. (a) What proportion of pregnancies last less than 270 days (about 9 months)? Please use 4 decimal places.) b) What proportion of pregnancies last between 240 and 270 days (roughly between 8 months and 9 months)'? (Please use 4 decimal places.) c)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 (d) What are the quartiles of the standard Normal distribution? (Use 2 decimal places.) Q3 = (e) What are the quartiles of the distribution of lengths of human pregnancies? Please use 2 decimal places Q1

Explanation / Answer

a) = 259, = 16

x = 270

P(X < 270) = P(Z < (X - )/) = P(Z < (270 - 259)/16) = P(Z < 0.6875) = 0.7541

b) P(240 < X < 270) = P(X<270) - P(X < 240) = 0.7541 - P(Z < (240 - 259)/16) = 0.7541 - P(Z < -1.1875)
= 0.7541 - 0.1175 = 0.6366

c) P(Z < (X - 259)/16) = 0.8, z = 0.8416
0.8416 = (X - 259)/16, X = 272.47 days

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

For Q1, p value is 0.25, z = -0.6745 = (x - 0)/1, x = -0.67

For Q3, p value is 0.75, z = 0.6745, x = 0.67

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