Question

In: Statistics and Probability

A random value is drawn from a normally distribution population with mean 28 and standard deviation...

A random value is drawn from a normally distribution population with mean 28 and standard deviation 2.

What is the probability that the value is:

a) greater than 30?

b) less than 24?

c) greater than 28?

d) equal to 27?

Solutions

Expert Solution

Solution :

Given that,

mean = = 28

standard deviation = = 2

(A)P(x >30 ) = 1 - P(x<30 )

= 1 - P[(x -) / < (30-28) /2 ]

= 1 - P(z <1 )

Using z table

= 1 - 0.8413

probability= 0.1587

(B)

P(X<24 ) = P[(X- ) / < (24-28) /2 ]

= P(z <-2 )

Using z table

=0.0228

probability=0.0228

= 1 - P[(x -) / < (28-28) /2 ]

= 1 - P(z <0 )

Using z table

= 1 - 0.5

probability= 0.5

(D)P(x=28 ) =0

probability=0

orchestra answered 2 years ago

Next > < Previous

Related Solutions

A random sample of 28 items is drawn from a population whose standard deviation is unknown....

A random sample of 28 items is drawn from a population whose standard deviation is unknown. The sample mean is x⎯⎯x¯ = 790 and the sample standard deviation is s = 15. Use Appendix D to find the values of Student’s t. (a) Construct an interval estimate of μ with 99% confidence. (Round your answers to 3 decimal places.) The 99% confidence interval is from to (b) Construct an interval estimate of μ with 99% confidence, assuming that s = 30....

A random sample is drawn from a population with mean μ = 70 and standard deviation...

A random sample is drawn from a population with mean μ = 70 and standard deviation σ = 5.8. [You may find it useful to reference the z table.] a. Is the sampling distribution of the sample mean with n = 17 and n = 43 normally distributed? Yes, both the sample means will have a normal distribution. No, both the sample means will not have a normal distribution. No, only the sample mean with n = 17 will have...

A random sample is drawn from a population with mean μ = 68 and standard deviation...

A random sample is drawn from a population with mean μ = 68 and standard deviation σ = 5.7. [You may find it useful to reference the z table.] a. Is the sampling distribution of the sample mean with n = 16 and n = 41 normally distributed? Yes, both the sample means will have a normal distribution. No, both the sample means will not have a normal distribution. No, only the sample mean with n = 16 will have...

A random sample is drawn from a population with mean μ = 72 and standard deviation...

A random sample is drawn from a population with mean μ = 72 and standard deviation σ = 6.0. [You may find it useful to reference the z table.] a. Is the sampling distribution of the sample mean with n = 17 and n = 45 normally distributed? Yes, both the sample means will have a normal distribution. No, both the sample means will not have a normal distribution. No, only the sample mean with n = 17 will have...

A random sample is drawn from a population with mean μ = 74 and standard deviation...

A random sample is drawn from a population with mean μ = 74 and standard deviation σ = 6.2. [You may find it useful to reference the z table.] a. Is the sampling distribution of the sample mean with n = 18 and n = 47 normally distributed? Yes, both the sample means will have a normal distribution. No, both the sample means will not have a normal distribution. No, only the sample mean with n = 18 will have...

Random variable X is drawn from a normal distribution with mean 13.59 and standard deviation 2.39....

Random variable X is drawn from a normal distribution with mean 13.59 and standard deviation 2.39. Calculate the probability of X being less than 11.31. What is the probability of X exceeding 12.52? What is the probability of X lying between 13.75 and 15.09? Verify your answers to parts 1 and 2 above using numerical sampling. (Harder) verify your answers to part 3 above using numerical sampling.

A random sample is drawn from a population with mean μ = 66 and a standard...

A random sample is drawn from a population with mean μ = 66 and a standard deviation σ =5.5. Are the sampling distribution of the sample mean with n = 16 and with n = 36 normally distributed? A. Yes, both the sample means will have a normal distribution. B. No, for both sample sizes, the standard normal distribution could not be used. C. No, the standard normal distribution could be used only for the sample size n = 16....

consider a normally distributed random variable with a population mean of 190 and a standard deviation...

consider a normally distributed random variable with a population mean of 190 and a standard deviation of 24. A sample mean of 36 observations will be taken the probability that the sample mean will be between 196 and 198 is?

A random sample is drawn from a normally distributed population with mean μ = 33 and...

A random sample is drawn from a normally distributed population with mean μ = 33 and standard deviation σ = 2.1. Use Table 1. a. Are the sampling distributions of the sample mean with n = 41 and n = 82 normally distributed? Yes No b. Can you use the standard normal distribution to calculate the probability that the sample mean is less than 33.6 for both sample sizes? Yes No c. Calculate the above probabilities for both sample sizes....

A random sample is drawn from a normally distributed population with mean μ = 27 and...

A random sample is drawn from a normally distributed population with mean μ = 27 and standard deviation σ = 2.1. [You may find it useful to reference the z table.] a. Are the sampling distribution of the sample mean with n = 35 and n = 70 normally distributed? Yes, both the sample means will have a normal distribution. No, both the sample means will not have a normal distribution. No, only the sample mean with n = 35...

Subjects