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
Delvig [45]
3 years ago
6

The times that customers spend in a book store are normally distributed with a mean of 39.5 minutes and a standard deviation of

15.9 minutes. A random sample of 60 customers has a mean of 36.1 minutes or less. Would this outcome be considered unusual, so that the store should reconsider its displays?
Mathematics
1 answer:
Juli2301 [7.4K]3 years ago
5 0

Answer:

Since |Z| = 1.66 < 2, this outcome should not be considered unusual.

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.

If |Z| > 2, X is considered unusual.

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 question, we have that:

\mu = 39.5, \sigma = 15.9, n = 60, s = \frac{15.9}{\sqrt{60}} = 2.05

A random sample of 60 customers has a mean of 36.1 minutes or less. Would this outcome be considered unusual, so that the store should reconsider its displays?

We have to find Z when X = 36.1.

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

By the Central Limit Theorem

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

Z = \frac{36.1 - 39.5}{2.05}

Z = -1.66

So |Z| = 1.66

Since |Z| = 1.66 < 2, this outcome should not be considered unusual.

You might be interested in
Determine if they triangles are similar. If so, by what Theorem?
marusya05 [52]

Answer:

SSS

Step-by-step explanation:

The sides of the smaller triangle equal the sides of the larger triangle when you multiply them by six, so they are parallel.

4 0
2 years ago
10 cookie someone eats 4 of them he ate what percentage of the cookies
Virty [35]

Answer:

40%

Step-by-step explanation:

10/4 = .4

.4 = 40%


4 0
3 years ago
4th grade math. Need help
Rasek [7]

Answer:2 whole sandwiches and 3/4 of another one


Step-by-step explanation:


8 0
3 years ago
Read 2 more answers
HELPPP!! PLSSS IM STUCK The vertices of a triangle are P(-7, -4), Q(-7, -8, and R(3, -3). Name the vertices of the image reflect
kvasek [131]
Reflection across the line y= x, cause to interchange the x and y coordinate
 p(x,y) ⇒ p(y,x)
8 0
3 years ago
What is 7 + 7 +7+7+7+7 x 0<br><br> XD
Pachacha [2.7K]
Uuuummm I think it’s a carrot?
5 0
3 years ago
Read 2 more answers
Other questions:
  • Does 2 dollar equal 100 Japanese yen?
    6·1 answer
  • A pet store has 10 puppies for every 6 kittens. What is the ratio of kittens to puppies?
    14·1 answer
  • What is 193.492 rounded to the nearest hundredth?
    11·2 answers
  • Angela needs $60 to buy a series of books. She has saved $24 and plans to work as a babysitter to earn $4 per hour. Which inequa
    7·2 answers
  • Use the figure below to enter the sides of triangle from largest to smallest. The shortest side is side:
    5·1 answer
  • The perimeter of a rectangle is 60 cm. The ratio of length to width is 3:2 . Find the length and width of the rectangle.
    5·1 answer
  • Wayne walked from the car dealership to the post office and then from the post office to the garbage dump. How far did Wayne wal
    15·2 answers
  • Circle O has a circumference of approximately 25077 ft.
    15·1 answer
  • Given m||n find the value of x.
    13·1 answer
  • I really need help with this question pls help
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!