Question

In: Statistics and Probability

6. Suppose that it is known that the mean cost for a certain medical procedure is...

6. Suppose that it is known that the mean cost for a certain medical procedure is $50,000 and that the standard deviation is $13,000.

(a) If you draw a random sample of 45 patients who underwent the same medical procedure, what is the sampling distribution for the sample mean cost based on these 45 patients? Justify your response in one sentence.

(b) What is the probability that the sample mean cost from these 45 patients is between $52,000 and $55,000?

Solutions

Expert Solution

Solution :

Given that,

mean = = 50000

standard deviation = = 13000

n = 45

(a)

sampling distribution of mean = = = 50000

sampling distribution of standard deviation = / n = = / n = 13000 / 45=1937.9

(b)

= 50000

= / n = 13000 / 45=1937.9

P(52000< <55000 ) = P[(52000-50000) / 1937.9< ( - ) / < (55000-50000) / 1937.9)]

= P(1.03 < Z <2.58 )

= P(Z < 2.58) - P(Z < 1.03)

Using z table,  

= 0.9951 -0.8485

probability = 0.1466


Related Solutions

Suppose it is known that in a certain population the mean systolic blood pressure (SBP) is...
Suppose it is known that in a certain population the mean systolic blood pressure (SBP) is 120 mmHg and the standard deviation is 10 mmHg. In a random sample of size 40 from this population, what is the probability that this sample will have a mean SBP greater than 124 mmHg?
A medical researcher wants to determine if the average hospital stay after a certain procedure is...
A medical researcher wants to determine if the average hospital stay after a certain procedure is less than 11.87 days. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≥ 11.87, Alternative Hypothesis: μ < 11.87. If the researcher randomly samples 25 patients that underwent the procedure and determines their average hospital stay was 10.6 days with a standard deviation of 6.724 days, what is the test statistic and p-value of this test? Question 10 options: 1) Test...
A certain medical test is known to detect 72% of the people who are afflicted with...
A certain medical test is known to detect 72% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?
A certain medical test is known to detect 73% of the people who are afflicted with...
A certain medical test is known to detect 73% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places? Assume that 39% of people are left-handed. If we...
A certain medical test is known to detect 50% of the people who are afflicted with...
A certain medical test is known to detect 50% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?
A certain medical test is known to detect 49% of the people who are afflicted with...
A certain medical test is known to detect 49% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?
The lifetimes of a certain electronic component are known to be normally distributed with a mean...
The lifetimes of a certain electronic component are known to be normally distributed with a mean of 1,400 hours and a standard deviation of 600 hours. For a random sample of 25 components the probability is 0.6915 that the sample mean lifetime is less than how many hours? A)1345 B)1460 C)1804 D)1790
Suppose it is known that the IQ scores of a certain population of adults are approxi-...
Suppose it is known that the IQ scores of a certain population of adults are approxi- mately normally distributed with a standard deviation of 15. A simple random sample of 25 adults drawn from this population had a mean IQ score of 105. a) Is there evidence at 5% significance level that the average IQ in this population is not equal to 100? Please also explain how you got the critical value. Thanks!!!
1. Suppose it is known that the IQ scores of a certain population of adults are...
1. Suppose it is known that the IQ scores of a certain population of adults are approxi- mately normally distributed with a standard deviation of 15. A simple random sample of 25 adults drawn from this population had a mean IQ score of 105. a) Would we be able to reject Ho if we were to test it at 1% significance level? Explain. b)Construct and interpret the 95% confidence interval for population average IQ from these data. c)Based on the...
Rockwell hardness of pins of a certain type is known to have a mean value of...
Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.5. (Round your answers to four decimal places.) (a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 16 pins is at least 51? (b) What is the (approximate) probability that the sample mean hardness for a random sample of 45 pins is at least 51?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT