Question

In: Statistics and Probability

Suppose that a population is known to be normally distributed with µ = 317 and σ...

Suppose that a population is known to be normally distributed with µ = 317 and σ = 90. If a random sample of size n = 50 is selected, calculate the probability that the sample mean is greater than 300.

Solutions

Expert Solution

Solution :

Given that,

mean = = 317

standard deviation = = 90

= =317

= / n = 90 / 50 = 12.73

P( >300 ) = 1 - P( < 300)

= 1 - P[( - ) / < (300-317) /12.73 ]

= 1 - P(z <-1.34 )

Using z table

= 1 - 0.0901

=0.9099

orchestra answered 3 years ago
Next > < Previous

Related Solutions

Suppose that a population is known to be normally distributed with μ =2,400 and σ=220. If...
Suppose that a population is known to be normally distributed with μ =2,400 and σ=220. If a random sample of size n=88 is​ selected, calculate the probability that the sample mean will exceed 2,500 ​P(x > 2,500​)= ​(Round to four decimal places as​ needed.)
Suppose µ is the mean of a normally distributed population for which the standard deviation is...
Suppose µ is the mean of a normally distributed population for which the standard deviation is known to be 3.5. The hypotheses H0 : µ = 10 Ha : µ 6= 10 are to be tested using a random sample of size 25 from the population. The power of an 0.05 level test when µ = 12 is closest to
A data set that X that is normally distributed with µ = 400 and a σ...
A data set that X that is normally distributed with µ = 400 and a σ = 20. (Show Work) a. What is P(370 < X < 410) = _________ b. Determine the value of X such that 70% of the values are greater than that value. _____
A data set that X that is normally distributed with µ = 400 and a σ...
A data set that X that is normally distributed with µ = 400 and a σ = 20.       a.  What is P(370 < X < 410) = _________     b. Determine the value of X such that 70% of the values are greater than that value. _____
A data set that X that is normally distributed with µ = 400 and a σ...
A data set that X that is normally distributed with µ = 400 and a σ = 20.     a.  What is P(370 < X < 410) = _________     b. Determine the value of X such that 60% of the values are greater than that value. _____ PLEASE SHOW ALL YOUR WORK
Suppose a population of scores x is normally distributed with μ = 16 and σ =...
Suppose a population of scores x is normally distributed with μ = 16 and σ = 5. Use the standard normal distribution to find the probability indicated. (Round your answer to four decimal places.) Pr(16 ≤ x ≤ 18.6)
Suppose a population of scores x is normally distributed with μ = 16 and σ =...
Suppose a population of scores x is normally distributed with μ = 16 and σ = 5. Use the standard normal distribution to find the probability indicated. (Round your answer to four decimal places.) Pr(16 ≤ x ≤ 18.3) You may need to use the table of areas under the standard normal curve from the appendix. Also, Use the table of areas under the standard normal curve to find the probability that a z-score from the standard normal distribution will...
The scores on a statistics test are Normally distributed with parameters µ = 75 and σ...
The scores on a statistics test are Normally distributed with parameters µ = 75 and σ = 10. Find the probability that a randomly chosen score is (a) no greater than 60 (b) at least 90 (c) between 60 and 90 (d) between 65 and 85 (e) at least 75
1)Test scores are normally distributed with µ = 65 and σ = 12. What is the...
1)Test scores are normally distributed with µ = 65 and σ = 12. What is the probability of a score above 50?. 2)Grades should be distributed as follows: 15% A, 20% B, 30% C, 20% D, and 15% F. If a class of 50 has 7 A’s, 15 B’s, 10 C’s, 15 D’s, and 3 F’s, is there statistically significant evidence that this class does not fit the ideal distribution?
Adult men’s heights (in inches) are normally distributed with µ = 69 and σ = 2.8....
Adult men’s heights (in inches) are normally distributed with µ = 69 and σ = 2.8. Adult women’s heights (in inches) are normally distributed with µ = 64 and σ = 2.5. Members of the “Beanstalk Club” must be at least six feet (72 inches) tall. If a man is selected at random, what is the probability that he is eligible for the Beanstalk Club? If a woman is selected at random, what is the probability that she is eligible...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT