Question

Length (in days) of human pregnancies is a normal random variable (X) with mean 266, standard deviation 16.

(It would be useful to sketch this normal distribution yourself, marking its mean and the values that are 1, 2, and 3 standard deviations below and above the mean. Click to compare your figure to ours)

The probability is 0.95 that a pregnancy will last between Select an answer 218 234 250 266 282 298   and Select an answer 218 234 250 266 282 298   days.

The shortest 16% of pregnancies last less than Select an answer 218 234 250 266 282 298   days.

The probability of a pregnancy lasting longer than 314 days is Select an answer 0.0015 0.025 0.16 0.68 0.95 0.997  .

There is a probability of 0.5 that a pregnancy will last longer than Select an answer 218 234 250 266 282 298   days.

Answer 1

a)

95% of observation of data lie within 2 std dev away from mean

µ =    266
σ =    16
X=Zσ + µ

X1 = -2 *   16   +   266   =   234
X2 = 2 *   16   +   266   =   298

so, answer is (234,298)

b)

68% of observation of data lie within 1 std dev away from mean

data left is equally distributed both sides i.e (16% both sides)

so, X=Zσ+µ = -1 *16+266 = 250(answer)

c)

Z=(x-µ)/σ=(314-266)/16=3

about 99.7% of observation of data lie within 3 std dev away from mean

data left (0.3%) equally distributed both sides i.e (0.15% data each side)

so, P(X>314) = 0.0015(answer)

d)

P(X>x) = 0.5

answer: 266 days