Question

In: Statistics and Probability

Given a distribution that has a mean of 40 and a standard deviation of 13, calculate...

Given a distribution that has a mean of 40 and a standard deviation of 13, calculate the probability that a sample of 49 has a sample mean that is no more than 35  

Solutions

Expert Solution

Solution :

Given that ,

mean =   = 40

standard deviation = = 13

n = 49

= 40

=  / n = 13/ 49=1.8571

P( <35 ) = P[( - ) / < (35-40) /1.8571 ]

= P(z < -2.69)

Using z table  

= 0.0036   

probability=  0.0036

orchestra answered 3 years ago
Next > < Previous

Related Solutions

A) If a normal distribution has a mean µ = 40 and a standard deviation σ...
A) If a normal distribution has a mean µ = 40 and a standard deviation σ = 2, what value of x would you expect to find 2 standard deviations below the mean B) If a normal distribution has a mean µ = 70 and a variance σ2 = 16, what value of x would you expect to find 2.5 standard deviations above the mean? C)If a sample yields a mean xmean = 44 and we know that the sum...
Suppose x has a distribution with a mean of 40 and a standard deviation of 21....
Suppose x has a distribution with a mean of 40 and a standard deviation of 21. Random samples of size n = 36 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has distribution with mean μx = and standard deviation σx = . (b) Find the z value corresponding to x = 47. z = (c) Find P(x < 47). (Round your answer to four decimal places.) P(x < 47)...
Suppose x has a distribution with a mean of 40 and a standard deviation of 28....
Suppose x has a distribution with a mean of 40 and a standard deviation of 28. Random samples of size n = 64 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has  ---Select--- a binomial an approximately normal a normal a geometric an unknown a Poisson distribution with mean μx = ? and standard deviation σx =  .? (b) Find the z value corresponding to x = 33. z = c) Find...
In a certain​ distribution, the mean is 40 with a standard deviation of 5 At least...
In a certain​ distribution, the mean is 40 with a standard deviation of 5 At least what fraction of the numbers are between the following pair of​ numbers? 30 and 50
Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of...
Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being 0.50 and n = 10. Either show work or explain how your answer was calculated. Use these formulas to do the hand calculations: Mean = np, Standard Deviation =  Comparison: Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being 0.10 and n = 10. Write a comparison of these statistics to those...
Given a standardized a normal distribution (with a mean of 0 and a standard deviation of...
Given a standardized a normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), what is that probability that a. Z is less than 1.57? b. Z is greater than 1.84? c. Z is between 1.57 and 1.84? d. Z is less than 1.57 or greater than 1.84?
Given the data below, calculate the mean, calculate the standard deviation and explain the significance of...
Given the data below, calculate the mean, calculate the standard deviation and explain the significance of each in the context of the data. Grade on Final Exam Frequency 50 1 60 2 70 3 80 5 90 6 100 3
Find the mean, variance, and standard deviation of the binomial distribution with the given values of...
Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n=70, p=0.6 The mean, μ, is _______  (Round to the nearest tenth as needed.) The variance, σ2, is _______ (Round to the nearest tenth as needed.) The standard deviation, σ, is _______ (Round to the nearest tenth as needed.)
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1),...
  Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1), complete parts (a) through (d) below.     a. What is the probability that Z is between - 1.56 and 1.88?   b. What is the probability that Z is less than - 1.56 or greater than 1.88?  c. What is the value of Z if only 6.5% of all possible Z values are larger?    d. Between what two values of Z (symmetrically distributed around...
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1),...
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1), complete parts (a) through (d). a. What is the probability that Z is less than 1.53? The probability that Z is less than 1.53 is _______ (Round to four decimal places as needed.) b. What is the probability that Z is greater than 1.84? The probability that Z is greater than 1.84 is _______  (Round to four decimal places as needed.) c. What is the probability that Z...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT