The length of human pregnancies from conception to birth follows a distribution

Question

The length of human pregnancies from conception to birth follows a distribution with mean 266 days and standard deviation 15 days.

1- Assume the distribution is bell-shaped (symmetric). The percent of pregnancies last between 236 and 281 days is approximately,                           [ Select ]                       ["81.5 %", "19.5%", "68%", "99.7%", "95%"]

2- - Assume the distribution is bell-shaped (symmetric). The percent of pregnancies last between 236 and 296 days is approximately,                           [ Select ]                       ["75%", "68%", "99.7%", "95%"]      

3- - Assume the distribution is not bell-shaped ( non symmetric). The percent of pregnancies last between 236 and 296 days is approximately,                            [ Select ]                       ["85%", "75%", "99.7%", "88.9%", "95%"]      

Explanation / Answer

z = (x-mean)/std deviation

1) For 236,

Z= (236-266)/15 = -2

For 281

Z= (281-266)/15 = 1

Thus, P(236 to 281) = P(-2<Z<1)

= 0.8413 - 0.0228 = 0.8185

approx 81.5%

2)

For 236,

Z= (236-266)/15 = -2

For 281

Z= (296-266)/15 = 2

Thus, P(236 to 296) = P(-2<Z<2)

= 0.9772 - 0.0228 = 0.9544

approx 95%

3)

Can't determine as nature of distribution is not known

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