Question

In: Statistics and Probability

The time a student sleeps per night has a distribution with mean 6.15 hours and a...

The time a student sleeps per night has a distribution with mean 6.15 hours and a standard deviation of 0.5 hours. Find the probability that average sleeping time for a randomly selected sample of 40 students is more than 6.29 hours per night. Answer: (keep 4 decimal places)

Solutions

Expert Solution

Solution :

mean = = 6.15

standard deviation = = 0.5

n = 40

=   = 6.15

= / n = 0.5 / 40 = 0.079

P( > 6.29) = 1 - P( < 6.29)

= 1 - P[( - ) / < (6.29 - 6.15) / 0.079 ]

= 1 - P(z < 1.77)

Using z table,    

= 1 - 0.9616

= 0.0384

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Consider the following problem for a student. Assume the student sleeps for 8 hours a day....
Consider the following problem for a student. Assume the student sleeps for 8 hours a day. The remaining 16 hours are to be allocated between study and leisure, other things equal. Let leisure be on the x-axis and study be on the y-axis. 1. Draw and label the axes appropriately and mark the point of origin. Then plot the straight line relationship between all possible combinations of study and leisure. 2. Calculate the slope of the line showing the relationship...
We know that the population distribution for the number of hours that Americans sleep per night...
We know that the population distribution for the number of hours that Americans sleep per night is normally distributed with a mean of 6.7 and a standard deviation of 1.4. a) What is the probability that a single, randomly draw observation (i.e., American) from this distribution sleeps less than 5 hours per night? b) What is the probability that a randomly drawn observation falls between 6 and 8 hours per night? c) What is the probability that a randomly draw...
If a study shows that the amount of time a student sleeps on any given nights...
If a study shows that the amount of time a student sleeps on any given nights is normally distributed with a mean of 7.2 hours and a standard deviation of 3 hours. Find the probability of one randomly selected student sleeping less than 8 hours.
The student union wants to determine the mean number of hours per week a student at...
The student union wants to determine the mean number of hours per week a student at Okanagan College studies. To accomplish this, they passed a questionnaire to 14 randomly chosen students among first and second year status. They also wanted insure an equal number of men and women to possibly investigate gender differences. The results were: Year of study 1 2 1 1 2 2 1 1 2 2 2 1 1 2 Mean hours studied per week 4 12...
The average time spent sleeping per night for a group of medical residents is 6.1 hours...
The average time spent sleeping per night for a group of medical residents is 6.1 hours with a standard deviation of 1.0 hour. Between what two values do the middle 50% of the sleep times fall?
Keith is a college student. He is extremely busy studying and working part-time. Keith sleeps in...
Keith is a college student. He is extremely busy studying and working part-time. Keith sleeps in late and therefore does not take time for breakfast. He rushes off to class. At lunch he has time for only French fries. When he gets home from school, he eats canned corn (only corn, nothing else) and washes it down with water. Then, he goes to work, only to start the same routine the next day. When Keith is confronted about his poor...
The National Survey of Student Engagement reported that the mean number of hours spent studying per...
The National Survey of Student Engagement reported that the mean number of hours spent studying per week for nursing majors is 18. Suppose a medical researcher obtained a random sample of 100 nursing majors, which yielded a sample mean study time of 19 19 hours. Assume the population standard deviation σ=10 hours. Test, using level of significance ?=0.05, whether the population mean study time for nursing majors is greater than 18 hours per week. ?crit= Find the test statistic ?data....
The length of time junior high school students sleep per night follows an approximate uniform distribution...
The length of time junior high school students sleep per night follows an approximate uniform distribution from seven to eleven hours. Suppose we randomly select a junior high student. 1. Find the probability that the randomly selected student sleeps less than 8 1/2 hours per night. A. 0. 375 B. 0. 4705 C. 0. 7727 D. . 2143 2. On average, how long does a junior high school student sleep per night ? A. 9 hours B. 8 hours C....
The belief is that the mean number of hours per week of part-time work of high...
The belief is that the mean number of hours per week of part-time work of high school seniors in a city is 10.4 hours. Data from a simple random sample of 28 high school seniors indicated that their mean number of part-time work was 11.5 with a standard deviation of 1.3. Test whether these data cast doubt on the current belief. (use α = 0.05) 1.) State your null and alternative hypotheses. 2.) State the rejection region. 3.) Calculate the...
The belief is that the mean number of hours per week of part-time work of high...
The belief is that the mean number of hours per week of part-time work of high school seniors in a city is 10.4 hours. Data from a simple random sample of 21 high school seniors indicated that their mean number of part-time work was 11.4 with a standard deviation of 1.2. Test whether these data cast doubt on the current belief. (use α = 0.05) Part a: State your null and alternative hypotheses. Part b: State the rejection region. Part...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT