Let ,
a)
; From standard normal probability table
b)
Since ,
...........(1)
From standard normal probability table
.............(2)
From (1) and (2) , We get ,
(C) Since , n=46
If , then
Therefore , the sampling distribution of sample mean is normal distribution
Where ,
d)
; From standard normal probability table
Assume that the duration of human pregnancies can be descibed by a Normal model with mean...
Assume that the duration of human pregnancies can be described by a normal model with mean 268 days and standard deviation 11 days. Answer the following questions. a) What percentage of pregnancies should last between 265 and 275 days? b) At least how many days should the longest 30% of all pregnancies last? c) Suppose a certain obstetrician is currently providing prenatal care to 60 pregnant women. Let y overbary represent the mean length of their pregnancies. According to the...
Assume that the duration of human pregnancies can be described by a normal model with mean 266 days and standard deviation 17 days. a) What percent of pregnancies should last between 275 and 290 days? b) At least how many days should the longest 20% of all pregnancies last? c) Suppose a certain doctor is currently providing prenatal care to 20 pregnant women. According to the Central Limit Theorem, what is the mean of the normal model of the distribution...
Assume that the duration of human pregnancies can be described by a normal model with mean 269 days and standard deviation 18 days. Answer the following questions a) What percentage of pregnancies should last between 265 and 280 days? % (Round to one decimal place as needed.)
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean of μ=271 days and standard deviation o=26 days. Complete parts (a) through (f) below. (a) What is the probability that a randomly selected pregnancy lasts less than 263 days? The probability that a randomly selected pregnancy lasts less than 263 days is approximately 0.3783. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer...
/53.) Length of pregnancies The length of human preg- nancies from conception to birth varies according to a distribution that is approximately Normal with mean 20-122 266 days and standard deviation 16 days. For each part, follow the four-step process. (a) At what percentile is a pregnancy that lasts 240 days (that's about 8 months)? (b) What percent of pregnancies last between 240 and 270 days (roughly between 8 months and 9 months)? (c) How long do the longest 20%...
Use R instead of a calculator for Questions 5 and 6. Please attach the R commands output and graphs that you used to answer the question. The R output alone is not an answer to the question. Please write a sentence or two to properly answer each question. Assume that the distribution of the duration of human pregnancies can be approxi- mated with a normal distribution with a mean of 266 days and a standard deviation of 16 days (a)...
1) The lengths of pregnancies in a small rural village are normally distributed with a mean of 263 days and a standard deviation of 15 days. A distribution of values is normal with a mean of 263 and a standard deviation of 15. What percentage of pregnancies last fewer than 295 days? P(X < 295 days) = % 2) The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is recorded in...
2. The length of human pregnancies from conception to birth varies according to a normal distribution with mean 272 days and standard deviation 19.5 days. (a) If one birth is selected at random, then find the probability the pregnancy lasted no more than 250 days. (15) (b) If 1000 births are randomly selected, then how many of the pregnancies would be expected to last no more than 250 days? ack to 3. (a) Referring to Problem 2, at least how...
8. The lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15 days. (a) Find the probability that an individual woman has a pregnancy shorter than 259 days. (b) If 36 women are randomly selected, find the probability that they have a mean preg- nancy shorter than 259 days. (c) There should be a difference in your method for the previous two questions. Explain what you did differently for each problem and...
8. The lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15 days. (a) Find the probability that an individual woman has a pregnancy shorter than 259 days. (b) If 36 women are randomly selected, find the probability that they have a mean preg- nancy shorter than 259 days. (c) There should be a difference in your method for the previous two questions. Explain what you did differently for each problem and...