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
gtnhenbr [62]
2 years ago
13

The average demand for rental skis on winter Saturdays at a particular area is 150 pairs, which has been quite stable over time.

There is variation due to weather conditions and competing areas; the standard deviation is 20 pairs. The demand distribution seems to be roughly normal.
(a) The rental shop stocks 170 pairs of skis. What is the probability that demand will exceed this supply on any winter Saturday?
(b) How many pairs of skis in stock does the shop have to have to make the probability in question (a) less than .01?
Mathematics
1 answer:
pentagon [3]2 years ago
6 0

Answer:

a) 15.87% probability that demand will exceed this supply on any winter Saturday

b) The shop needs to have 197 pairs of skis in stock.

Step-by-step explanation:

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.

In this problem, we have that:

\mu = 150, \sigma = 20

(a) The rental shop stocks 170 pairs of skis. What is the probability that demand will exceed this supply on any winter Saturday?

This probability is 1 subtracted by the pvalue of Z when X = 150. So

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

Z = \frac{170 - 150}{20}

Z = 1

Z = 1 has a pvalue of 0.8413

1 - 0.8413 = 0.1587

15.87% probability that demand will exceed this supply on any winter Saturday

(b) How many pairs of skis in stock does the shop have to have to make the probability in question (a) less than .01?

This is X when Z has a pvalue of 0.99.

So X when Z = 2.33

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

2.33 = \frac{X - 150}{20}

X - 150 = 2.33*20

X = 196.6

Rounding up, since the number of pairs is a discrete number

The shop needs to have 197 pairs of skis in stock.

You might be interested in
The scores on an achievement test are normaly distributed with mean µ = 100 and standard deviation σ = 100. What should the scor
ser-zykov [4K]

Answer:

the student should score atleast 229 to be among the top 10%.

Step-by-step explanation:

in terms of the normal distribution, and if the table that you're using calculates the area of the normal distribution from the mean to a point x, only then what we are actually finding the value 'x' at which the z-score is at 40% (the rest 50% is already skipped by the table)

P(0.4) = \dfrac{x - \mu}{\sigma}

after finding the the value at this z-score, we can find the value of x at which the score is in the top 10% range.

we can find the z-score either using a normal distribution table or calculator. (but be sure what area is it calculating)

looking at the table the closest value we can find is, 0.4015 at z = 1.29 ((it is above 40% because we want to be in the top 10% range)

P(0.4015) = \dfrac{x - 100}{100}

1.29 = \dfrac{x - 100}{100}

x = 1.29(100) + 100

x = 229

the student should score atleast 229 to be among the top 10%.

7 0
2 years ago
Help help help its baby work
Olenka [21]

Answer:

the volume of the larger cube is 512

Step-by-step explanation:

we plug in the value of the side into the equation

so we get

8 x 8 x 8= 512

hope this helps <3

6 0
3 years ago
Plz help, really would appreciate it!!! =]
Nonamiya [84]

Answer:

144 x 7 = 1008

The train can hold 1008 people

Mark brainlest

Step-by-step explanation:

4 0
2 years ago
The figure below shows a large block of cheese. Cheese Block 10 inches 4 inches 6 inches What is the volume of the block of chee
Masja [62]

Answer:120 cubic inches

Step-by-step explanation:

(4*10)*6 (40*6)/2 240/2=120 cubic inches

8 0
3 years ago
100 points! show work or else i report
butalik [34]

Answer:

Step-by-step explanation:

A frozendinner requires 4.0 minutes to heat on full power.(a) How much electrical energy ( in kWh) is used?(b) If the cost of electricity is 12 cents per kWh, ...

6 0
2 years ago
Other questions:
  • Let each Square represent 1/3 unit by 1/3 unit.
    12·1 answer
  • At the movie theater, child admission is $5.30 and adult admission is $9.10. On Tuesday, three times as many adult tickets were
    12·1 answer
  • 7s. 49
    7·1 answer
  • What is 5 / 43 / 25 / 86
    5·1 answer
  • 6. Evaluate /(x) = -4x - 5 for x = -1.
    8·1 answer
  • Round 462093 to the nearest 10 000
    6·1 answer
  • What is the value of -2/5 / 3/4?
    7·1 answer
  • PLZ HELP, 20 POINTS, WILL GIVE YOU BRAINLIEST!!!
    15·1 answer
  • Two triangles are similar. The sides of the first triangle are 8, 9 and 12. The smallest side of the second triangle is 6. Find
    7·1 answer
  • Amir drove from Jerusalem to the lowest place on Earth, the Dead Sea. His altitude relative to sea level (in meters) as a functi
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!