Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 13 days. a) What percentage of pregnancies should last between 271 and 284 days? b) At least how many days should the longest 20% of all pregnancies last? c) Suppose a certain obstetrician is currently providing prenatal care to 48 pregnant women. Let y represent the mean length of their pregnancies. According to the Central Limit Theorem, what's the distribution of this sample mean, y? Specify the model, mean, and standard deviation. d) What's the probability that the mean duration of these patients' pregnancies will be less than 263 days?

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Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 13 days.
a) What percentage of pregnancies should last between 271 and 284 days?
b) At least how many days should the longest 20% of all pregnancies last?
c) Suppose a certain obstetrician is currently providing prenatal care to 48 pregnant women. Let y represent the mean length of their pregnancies. According to the Central Limit Theorem,
what's the distribution of this sample mean, y? Specify the model, mean, and standard deviation.
d) What's the probability that the mean duration of these patients' pregnancies will be less than 263 days?
Transcribed Image Text:Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 13 days. a) What percentage of pregnancies should last between 271 and 284 days? b) At least how many days should the longest 20% of all pregnancies last? c) Suppose a certain obstetrician is currently providing prenatal care to 48 pregnant women. Let y represent the mean length of their pregnancies. According to the Central Limit Theorem, what's the distribution of this sample mean, y? Specify the model, mean, and standard deviation. d) What's the probability that the mean duration of these patients' pregnancies will be less than 263 days?
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