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
PSYCHO15rus [73]
2 years ago
6

According to a report from a business intelligence company, smartphone owners are using an average of 22 apps per month. Assume

that number of apps used per month by smartphone owners is normally distributed and that the standard deviation is 4. Complete parts (a) through (d) below. If you select a random sample of 36 smartphone owners, what is the probability that the sample mean is between 21 and 22?
Mathematics
1 answer:
Ira Lisetskai [31]2 years ago
4 0

Answer:

0.4332 = 43.32% probability that the sample mean is between 21 and 22.

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.

According to a report from a business intelligence company, smartphone owners are using an average of 22 apps per month.

This means that \mu = 22

Standard deviation is 4:

This means that \sigma = 4

Sample of 36:

This means that n = 36, s = \frac{4}{sqrt{36}}

What is the probability that the sample mean is between 21 and 22?

This is the p-value of Z when X = 22 subtracted by the p-value of Z when X = 21.

X = 22

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

By the Central Limit Theorem

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

Z = \frac{22 - 22}{\frac{4}{sqrt{36}}}

Z = 0

Z = 0 has a p-value of 0.5.

X = 21

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

Z = \frac{21 - 22}{\frac{4}{sqrt{36}}}

Z = -1.5

Z = -1.5 has a p-value of 0.0668.

0.5 - 0.0668 = 0.4332

0.4332 = 43.32% probability that the sample mean is between 21 and 22.

You might be interested in
Picture below! <br> What is the equation of the line in slope-intercept form?<br> y = __x +__
weqwewe [10]

the equation of the line is y = 3/5x + 3

8 0
3 years ago
Write an equation of the line that passes through the points (−3,−4) and (0,2).
Leno4ka [110]
It should be y=2x+2 it has to be in slope form: y=mx+b
4 0
3 years ago
Read 2 more answers
There are two possible offers that could be applied to orange juice that would each explain this reduction in the total bill. 4:
svlad2 [7]

Incomplete question. The full question read;

My local store sometimes runs offers on some of its products. There are three different types of  offers that could be in place:

  • Buy a certain number of a particular product and get an extra one for half price.
  • A percentage discount (always a multiple of 5%) on one particular product.
  • A percentage discount (always a multiple of 5%) on purchases worth a total of more than $10.

The store only ever has one of these offers in place at any time.

Last week I bought

  • 3 cartons of orange juice for $4 each
  • 1 loaf of bread for $3
  • 5 packets of snacks for $1 each

This week I bought the same set of items, but only paid $18 even though the individual items still had the same price.

(4) There are two possible offers that could be applied to orange juice that would each explain this reduction in the total bill.

What are these two offers?

(5) What are the other two offers that could explain the reduction in the total bill?

Answer:

<u>1. Buy a certain number of a particular product and get an extra one for half price</u>

Step-by-step explanation:

By buying 2 and getting one at half the price matches the offer:

  • Buy a certain number of a particular product and get an extra one for half price.

This means two (2) cartons of orange juice cost $8 (4*2) + $2 cost the extra one at half price.

6 0
3 years ago
What is the answer. please help
zubka84 [21]

Answer:

Exact Form:−2/3

Decimal Form:−0.666…

Step-by-step explanation:

6 0
1 year ago
Read 2 more answers
A. Only sequence A<br> B. Only sequence B<br> C. Both<br> D. Neither<br> 30 POINTS OMG
Phoenix [80]
B. Only Sequence B

The one with the reflection over the line HI and then the 6 unit translation to the right
7 0
2 years ago
Read 2 more answers
Other questions:
  • What causes a line to switch direction? Changing the slope from a whole number to a fraction. Changing the y-intercept from nega
    12·1 answer
  • Terri wrote the equation using slope-intercept form for the line that passes through the points (4,6) and (-2,3). Which best des
    15·1 answer
  • We will forget this knowledge of what we learned when were older.
    5·1 answer
  • In which situation is it appropriate to use taxicab geometry instead of euclidean geometry?
    8·1 answer
  • Select the two binomals that are factors of this trinomial x^2+8x+12
    7·1 answer
  • Use fraction strips to write 2 4/5 as an equivalent improper fraction.
    8·1 answer
  • Does the point (5, 0) satisfy the equation y=x​
    5·2 answers
  • Please help me with this surds question. Explain how you got your answer.
    8·1 answer
  • Solve for the value of r help pls
    15·1 answer
  • At a carnival a food stall sold bags of cotton candy for $5 each and bags of popcorn for $7 each. A total of 140 bags were sold
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!