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
Leokris [45]
3 years ago
14

Suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. A samp

le of 100 steady smokers revealed that the sample mean is $20. The population standard deviation is $5. What is the probability that a sample of 100 steady smokers spend between $19 and $21
Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
6 0

Answer:

95.44% probability that a sample of 100 steady smokers spend between $19 and $21

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 normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this problem, we have that:

\mu = 20, \sigma = 5, n = 100, s = \frac{5}{\sqrt{100}} = 0.5

What is the probability that a sample of 100 steady smokers spend between $19 and $21

This is the pvalue of Z when X = 21 subtracted by the pvalue of Z when X = 19. So

X = 21

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

By the Central Limit Theorem

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

Z = \frac{21 - 20}{0.5}

Z = 2

Z = 2 has a pvalue of 0.9772

X = 19

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

Z = \frac{19 - 20}{0.5}

Z = -2

Z = -2 has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

95.44% probability that a sample of 100 steady smokers spend between $19 and $21

You might be interested in
Look at the pic help
Ivenika [448]

Answer:-68 i think

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Which of the following describes the dimensions of a backyard?
emmainna [20.7K]

Answer:

the lengths of the sides of the yard.

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
What is 1.28 as a fraction. Simplify
attashe74 [19]
128/100=32/25
..................
8 0
3 years ago
Read 2 more answers
What is the standard error of a sampling distribution with a population standard deviation of 12 and the sample size of 81?
Marizza181 [45]

Answer: d. 1.3333

Step-by-step explanation:

We know that the standard error of a sampling distribution is given by :-

S.E.=\dfrac{\sigma}{\sqrt{n}}

, where \sigma = Population standard deviation.

n= Sample size.

AS per given , we have

\sigma =12

n=81

Then, the standard error of a sampling distribution with a population standard deviation of 12 and the sample size of 81 will be :-

S.E.=\dfrac{12}{\sqrt{81}}

=\dfrac{12}{\sqrt{9^2}}=\dfrac{12}{9}\\\\=\dfrac{4}{3}\\\\\approx1.3333

Hence, the standard error of a sampling distribution with a population standard deviation of 12 and the sample size of 81 is 1.3333.

Thus the correct answer is d. 1.3333 .

6 0
3 years ago
What is 12 1/2 as an improper fraction??
Olegator [25]
<span>To convert 12.5 to a fraction, consider the decimal portion of the number, .5. Since .5 is in the tenth spot of the decimal, it may be read as five-tenths, or 5/10. To reduce it to lowest terms, find the lowest common denominator, 5, and divide each by that number to get 1/2, or one-half. Thus, the number is now 12 1/2. To convert this mixed number into an entirely rational fraction, multiply the whole number, 12, by the denominator, 2, to get 24, then add the numerator, to end up with 25. This is the new numerator, so the rational number is 25/2. To check the work, divide 25 by 2 on a calculator or as a decimal equation, yielding 12.5.</span>
5 0
3 years ago
Other questions:
  • What is the value of h?<br> 4<br> 8sqrt3<br> 16<br> 8srt2
    14·2 answers
  • What is 8640 minutes in days? remember there are 60 minutes in an hour and 24 hours in a day. CAN SOMEONE HELP!?
    15·2 answers
  • The mean hourly salary of the 10 employees at a fast­food restaurant is $8.25. One of the employees earning $6.50 an hour leaves
    15·1 answer
  • Identify the volume of the hemisphere in terms of π. HELP PLEASE!!
    11·1 answer
  • on monday, steve read 9 pages of his new book. to finish the first chapter on tuesday, he needs to read double the number of pag
    11·1 answer
  • There are 4 red and 6 green marbles in a jar. What is the probability of drawing two green marbles, with replacement?
    7·1 answer
  • Need help on problem 10
    12·1 answer
  • In the figure shown, what fractional part of the circle is shaded?
    9·2 answers
  • The ratio of boys to girls in a class is 7:5. There are 36 students in the class. How many
    5·2 answers
  • Lucas bought an 8 pack if bottled iced tea. Each bottle contained 14.75 fluid ounces. What was the totals number of fluid ounces
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!