Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=117 days and standard deviation σ=11 days. Complete parts (a) through ( f ) below. C. If 100 independent random samples of size n=33 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 113 days. (e) What might you conclude if a random sample of 33 pregnancies resulted in a mean gestation period of 113 days or less? This result would be so the sample likely came from a population whose mean gestation period is 117 days. (f) What is the probability a random sample of size 19 will have a mean gestation period within 10 days of the mean? The probability that a random sample of size 19 will have a mean gestation period within 10 days of the mean is (Round to four decimal places as needed.)
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=117 days and standard deviation σ=11 days. Complete parts (a) through ( f ) below. C. If 100 independent random samples of size n=33 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 113 days. (e) What might you conclude if a random sample of 33 pregnancies resulted in a mean gestation period of 113 days or less? This result would be so the sample likely came from a population whose mean gestation period is 117 days. (f) What is the probability a random sample of size 19 will have a mean gestation period within 10 days of the mean? The probability that a random sample of size 19 will have a mean gestation period within 10 days of the mean is (Round to four decimal places as needed.)
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=117 days and standard deviation σ=11 days. Complete parts (a) through ( f ) below. C. If 100 independent random samples of size n=33 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 113 days. (e) What might you conclude if a random sample of 33 pregnancies resulted in a mean gestation period of 113 days or less? This result would be so the sample likely came from a population whose mean gestation period is 117 days. (f) What is the probability a random sample of size 19 will have a mean gestation period within 10 days of the mean? The probability that a random sample of size 19 will have a mean gestation period within 10 days of the mean is (Round to four decimal places as needed.)
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=117 days and standard deviation σ=11 days. Complete parts (a) through ( f ) below. C. If 100 independent random samples of size n=33 pregnancies were obtained from this population, we would expect sample(s) to have a sample mean of exactly 113 days. (e) What might you conclude if a random sample of 33 pregnancies resulted in a mean gestation period of 113 days or less? This result would be so the sample likely came from a population whose mean gestation period is 117 days. (f) What is the probability a random sample of size 19 will have a mean gestation period within 10 days of the mean? The probability that a random sample of size 19 will have a mean gestation period within 10 days of the mean is (Round to four decimal places as needed.)
Transcribed Image Text:Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ = 117 days and standard deviation = 11 days. Complete parts (a) through (f) below.
OC. If 100 independent random samples of size n = 33 pregnancies were obtained from this population, we would expect
(e) What might you conclude if a random sample of 33 pregnancies resulted in a mean gestation period of 113 days or less?
This result would be unusual, so the sample likely came from a population whose mean gestation period is less than
(f) What is the probability a random sample of size 19 will have a mean gestation period within 10 days of the mean?
The probability that a random sample of size 19 will have a mean gestation period within 10 days of the mean is 0.0001
(Round to four decimal places as needed.)
C
sample(s) to have a sample mean of exactly 113 days.
117 days.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
Expert Solution
Step 1
Given:
Mean
Standard deviation
A Z-score is a measure that indicates how many standard deviations away, a data value is, from the mean. It is given by the formula:
