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
zhannawk [14.2K]
3 years ago
8

In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces

, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
a. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?b. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?c. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?d. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?
Mathematics
1 answer:
nadya68 [22]3 years ago
5 0

Answer:

a) 0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less

b) 0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

c) 0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours

d) 86 should have a battery life of at least 9 hours.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

P(X \leq x) = \frac{x - a}{b-a}

The probability of being higher than x is:

P(X > x) = \frac{b - x}{b-a}

The probability of being between c and d is:

P(c \leq X \leq d) = \frac{d-c}{b-a}

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

This means that a = 8.5, b = 12

a. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

P(X \leq x) = \frac{x - a}{b-a}

P(X \leq 10) = \frac{10 - 8.5}{12 - 8.5} = 0.4286

0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less.

b. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

P(X > x) = \frac{b - x}{b-a}

P(X > 11) = \frac{12 - 11}{12 - 8.5} = 0.2857

0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

c. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

P(c \leq X \leq d) = \frac{d-c}{b-a}

P(9.5 \leq X \leq 11.5) = \frac{11.5 - 9.5}{12 - 8.5} = 0.5714

0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours.

d. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

Proportion of iPad Minis with a battery life of at least 9 hours.

P(X > 11) = \frac{12 - 9}{12 - 8.5} = 0.8571

Out of 100:

0.8571*100 = 85.71

To the nearest whole number

86 should have a battery life of at least 9 hours.

You might be interested in
A model rocket is launched with an initial velocity of 200 ft per second. The height h, in feet, of the rocket t seconds after t
Solnce55 [7]

Answer:

2.10 s, 10.40 s.

Step-by-step explanation:

We know that the height of the rocket is given by the function:

h=-16t^2+200t

We are asked to find the time for which the height of the rocket will be 350 ft. So, for that moment, we know the height but we don't know the time; however, we know that the equation can help us to find the time, doing h=350:

350=-16t^2+200t

The last is a quadratic equation, which can be put in the form at^2+bt+c=0 and solved applying the formula:

t=\frac{-b+-\sqrt{b^2-4ac} }{2a}

So, let's put the equation on the form at^2+bt+c=0 adding 16t^2 and subtracting 200t to each side of the equation; the result is:

16t^2-200t+350=0

So, we note that a=16, b=-200, and c=350.

Then,

t_1=\frac{200-\sqrt{200^2-4*16*350} }{2*16}=2.10

t_2=\frac{200+\sqrt{200^2-4*16*350} }{2*16}=10.40

According to the equation, that are the times for which the height will be 350 ft; that is because the rocket is going to ascend and then to fail again to the ground.

4 0
3 years ago
Suppose you go out to eat with a friend and your bill was $25.67. The local sales tax rate is 7% and you want to leave a 20% tip
Zina [86]

Answer:

Umm I'm not sure is it 25...

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Which points are generated by the function y = -5x + 2? Check all that apply. (2, 8) (2, -8) (13, 3) (3, -13)
Zanzabum
(2,-8) (3,-13) because if you plug them all in there the only ones that come out right 

4 0
3 years ago
Read 2 more answers
Please help i have a 15 percent in math please ill give brainliest
dusya [7]
32.92 next is 27 last is 230
7 0
2 years ago
Geometry help! Will give brainliest!! The slope of line b is -1/6. What is the slope of the line parallel to line b?
atroni [7]

Answer:

-1/6

Step-by-step explanation:

Parallel lines are lines which have the exact same slope but different y-intercepts. This means any line which is parallel and does not cross will have the exact same slope of -1/6.

3 0
3 years ago
Other questions:
  • 12 cups water ÷ 4 tablespoons lemonade mix
    14·1 answer
  • Tom took four seconds to run 6 yards Diane ran 5 yards in three seconds if they continue to run at the same speed who were to ge
    12·2 answers
  • Help me with this question plzzzz
    13·1 answer
  • Write an equation of the line that passes through (2, 7) and (0, −5)<br><br><br> y=
    5·2 answers
  • What is 1.66666666667 rounded to the nearest tenth
    7·1 answer
  • If the ratio of the surface areas of two similar geometrical solids is given by 121:36, what is the
    14·1 answer
  • State how many significant figures are proper in the results of the following calculations: (a) (106.7)(98.2)/(46.210)(1.01) (b)
    6·1 answer
  • Which phrase represents 3y +9
    13·1 answer
  • On a scale drawing,1 in represents 8 feet. What is the actual length of a room that measures 3.4 inches
    15·1 answer
  • Two numbers differ by 3. Their product<br> is 28. Find the numbers.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!