Question

In: Statistics and Probability

A set of data is normally distributed with a mean of 37 and a standard deviation...

A set of data is normally distributed with a mean of 37 and a standard deviation of 1.5. If you randomly select a data point and it is 37.75, which of the following would describe that data point?

Unusually large (Statistically significant)
Unusually small (Statistically significant)
Not unusual (Not statistically significant)
Not enough information

Expert Solution

Solution:

We are given that: a set of data is normally distributed with a mean of 37 and a standard deviation of 1.5.

That is: Mean = and standard deviation =

A data point is randomly selected and it is 37.75

That is: x = 37.75

We have to describe this data point

Note that: a number is unusually high or unusually low if it is more than 2 standard deviation from the mean and we can say a number is statistically significant.

If it is less than 2 standard deviation from the mean value, then we say this number is not unusual and it is not statistically significant.

z score gives number of standard deviations from the mean value for any x value.

Thus we use z score formula to find number of standard deviations.

Thus x = 37.75 is 0.5 standard deviation from the mean value and it is within +/- 2 standard deviation from mean value.

Thus correct description of the data point is:

Not unusual (Not statistically significant)

orchestra answered 1 year ago

A set of exam scores is normally distributed with a mean = 82 and standard deviation...

A set of exam scores is normally distributed with a mean = 82 and standard deviation = 4. Use the Empirical Rule to complete the following sentences. 68% of the scores are between and . 95% of the scores are between and . 99.7% of the scores are between and . LicensePoints possible: 3 This is attempt 1 of 3.

A set of exam scores is normally distributed with a mean = 80 and standard deviation...

A set of exam scores is normally distributed with a mean = 80 and standard deviation = 8. Use the Empirical Rule to complete the following sentences. 68% of the scores are between and . 95% of the scores are between and . 99.7% of the scores are between and . Get help: Video

a. A population is normally distributed with a mean of 16.4 and a standard deviation of...

a. A population is normally distributed with a mean of 16.4 and a standard deviation of 1.4. A sample of size 36 is taken from the population. What is the the standard deviation of the sampling distribution? Round to the nearest thousandth. b. A population is normally distributed with a mean of 15.7 and a standard deviation of 1.4. A sample of size 24 is taken from the population. What is the the standard deviation of the sampling distribution? Round...

1) Suppose a normally distributed set of data has a mean of 179 and a standard...

1) Suppose a normally distributed set of data has a mean of 179 and a standard deviation of 17. Use the 68-95-99.7 Rule to determine the percent of scores in the data set expected to be below a score of 213. Give your answer as a percent and includeas many decimal places as the 68-95-99.7 rule dictates. (For example, enter 99.7 instead of 0.997.) 2) Suppose a normally distributed set of data with 2800 observations has a mean of 100...

(a) Assume a population’s quantitative data values are normally distributed with mean µ and standard deviation...

(a) Assume a population’s quantitative data values are normally distributed with mean µ and standard deviation σ, and samples are simple random. Sketch 3 sampling distributions of sample means of sample size n for n = 1, n = 100, and n = 10,000, using continuous normal distribution curves. The sketches are not meant to be quantitatively precise—you just need to illustrate certain phenomena that occur as n increases. State the mean, standard deviation, and area under the curve for...

If X is normally distributed with a mean of 30 and a standard deviation of 2,...

If X is normally distributed with a mean of 30 and a standard deviation of 2, find P(30 ≤ X ≤ 33.4). a) 0.455 b) 0.855 c) 0.955 d) 0.555 e) 0.755 f) None of the above

X is normally distributed with a mean of -9.74 and a standard deviation of 0.27. a....

X is normally distributed with a mean of -9.74 and a standard deviation of 0.27. a. Find the value of x that solves P(X ≤ x)= 0.25 b. Find the value of x that solves P(X > x)= 0.20 c. Find the value of x that solves P(x <X ≤ -9.70) = 0.20 d. Find the value of x that solves P(-9.74 < X ≤x) = 0.35

Suppose that X is normally distributed with a mean of 50 and a standard deviation of...

Suppose that X is normally distributed with a mean of 50 and a standard deviation of 12. What is P(X ≥ 74.96) a) 0.481 b) 0.019 c) 0.981 d) 0.024 e) 0.020 f) None of the above

Assume that X is normally distributed with a mean of 5 and a standard deviation of...

Assume that X is normally distributed with a mean of 5 and a standard deviation of 4. Determine the value for x P(-x < X-5 < x) = 0.99 Can someone please explain in detail how to solve it with the help of the Cumulative Normal Distribution Table? Thanks!

1. A population is normally distributed with a mean of 18 and a standard deviation of...

1. A population is normally distributed with a mean of 18 and a standard deviation of 2.5. What is the probability of randomly selecting one item from the population having: a) A value greater than 18. b) A value between 14 and 21.