1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
madam [21]
3 years ago
6

If a normally distributed population has a mean (mu) that equals 100 with a standard deviation (sigma) of 18, what will be the c

omputed z-score with a sample mean (x-bar) of 106 from a sample size of 9?
Mathematics
1 answer:
garik1379 [7]3 years ago
7 0

Answer:

Z = 1

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean (mu) that equals 100 with a standard deviation (sigma) of 18

\mu = 100, \sigma = 18

Sample of 9:

This means that n = 9, s = \frac{18}{\sqrt{9}} = 6

What will be the computed z-score with a sample mean (x-bar) of 106?

This is Z when X = 106. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{106 - 100}{6}

Z = 1

So Z = 1 is the answer.

You might be interested in
three tanks are capable of holding 108 168l and 180 litre of milk determine the capacity of the greatest resource which can be u
SOVA2 [1]

Answer:

Nrrhrhfbbffnjtfjruhd

Step-by-step explanation:d dbrhrhrhdvrhrhrhrbfbfbrj

4 0
3 years ago
Write 240 and 1500 as products of their prime factor
Marina CMI [18]
240 = 2 × 120
120 = 2 × 60
60 = 2 × 30
30 = 2 × 15
15 = 3 × 5
The 2, 2, 2, 2, 3 and 5 are all the prime factors of 240. So, 2^4 × 3 × 5

1500 = 3 × 500
500 = 5 × 100
100 = 5 × 20
20= 5 × 4
4 = 2 × 2
The 3, 5, 5, 5, 2 and 2 are all the prime factors of 1500. So, 2² + 3 + 5³
4 0
3 years ago
Read 2 more answers
the african bush elephant weighs between 4.4 tons and 7.7 tons.what are its least and greatest weights rounded to the nearest to
ruslelena [56]
The average would be from 4 tons to 8 tons.
4 0
3 years ago
A standard six sided dice is rolled. What is te probability of rolling a 3 OR a 5
Vikki [24]

Answer:

1/3

Step-by-step explanation:

Rolling a die has the possible outcomes of 1,2,3,4,5,6 = 6 total

P(3 or 5) = number of  3 or 5's / total

              = 2/6

                = 1/3

5 0
3 years ago
Read 2 more answers
If you help me I will help you just message me
Leviafan [203]

Answer:

i hel32hhfkhf2ehkf e2k fe2kn fkne2 fe2fn3  3 3juur3jke

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • Which number is an irrational number
    11·2 answers
  • The store has 28 notebooks in packs of 4. Three packs of notebooks are sold. How many packs of notebooks are left?
    11·2 answers
  • A diver needs to descend to a depth of 100 feet below sea level. She wants to do it in 5 equal descents. How far should she trav
    8·1 answer
  • 1/4 rounded to the nearest whole number
    5·2 answers
  • Ok what is 4 1/8 - 3/4
    11·2 answers
  • G Image result for pe.
    15·1 answer
  • Melissa wants to put a bird bath in her yard at point (x, y), and wants it to be is inside the enclosed shaded area shown in the
    8·1 answer
  • I'm bored.....................
    6·2 answers
  • A square-based pyramid has a base side length of 10 feet and a height of 21 feet.
    15·1 answer
  • PLEASE HELP<br> Given g(x) = –? – 2, find g(3).
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!