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Anna [14]
3 years ago
6

I really need help please.

Mathematics
1 answer:
love history [14]3 years ago
6 0

Answer:

64

Step-by-step explanation:

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The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2inches.a. Wha
Charra [1.4K]

Answer:

a)P(X>66)=P(Z>1)=1-P(Z

b)P(\bar X >66)=P(Z>2)=1-P(Z

c) P(\bar X >66)=P(Z>10)=1-P(Z

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

2) Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(64,2)  

Where \mu=64 and \sigma=2

We are interested on this probability

P(X>66)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>66)=P(\frac{X-\mu}{\sigma}>\frac{66-\mu}{\sigma})=P(Z>\frac{66-64}{2})=P(Z>1)

And we can find this probability on this way:

P(Z>1)=1-P(Z

3) Part b

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

P(\bar X >66)=P(Z>\frac{66-64}{\frac{2}{\sqrt{4}}}=2)

And using a calculator, excel or the normal standard table we have that:

P(Z>2)=1-P(Z

4) Part c

P(\bar X >66)=P(Z>\frac{66-64}{\frac{2}{\sqrt{100}}}=10)

And using a calculator, excel or the normal standard table we have that:

P(Z>10)=1-P(Z

3 0
3 years ago
3/4 + 1/12 helppppppppppppppp
Crank

Answer:

The answer is 5/6.

Step-by-step explanation:

4 0
3 years ago
This year a business hade a profit of $10,000. The profit is expected to increase by 12% each year. What will be the profit in s
Margarita [4]

Answer:

Question 858558: a buisness had $10,000 profit in 2000. then the profit increased by 8% each year for the next 10 years. write a function that models the profit in dollars over time Answer by josmiceli(19441) (Show Source):

4 0
3 years ago
What is the sum of the first 4 terms of the arithmetic sequence in which the 8th term is 10 and the 14th term is 29.5?
Sholpan [36]

Answer:

Sum of the first 4 terms is

14.50

Explanation:

In an arithmetic sequence, whose first term is

a

and difference between a term and its preceding term is

d

,

the

n

t

h

term is

a

+

(

n

−

1

)

d

and sum of first

n

terms is

n

2

(

2

a

+

(

n

−

1

)

d

)

Hence

6

t

h

term will be

a

+

5

d

=

8

and

10

t

h

term will be

a

+

9

d

=

13

Subtracting first from second,

4

d

=

5

or

d

=

1.25

and

a

=

8

−

5

⋅

1.25

=

8

−

6.25

=

1.75

Hence sum of first four terms is

4

2

⋅

(

2

⋅

1.75

+

3

⋅

1.25

)

=

2

⋅

(

3.5

+

3.75

)

=

2

⋅

7.25

=

14.50

8 0
2 years ago
Jill arranges quarters in stacks of increasing powers of 2,starting with the zeroth power (2^0).If she ends up with six stacks,h
bearhunter [10]
2⁰ =  1
2¹ =  2
2² =  4
2³ =  8
2⁴ = 16
2⁵ = 32

The sum  =  (the next power of 2) - 1

                     2⁶ - 1  =  63 .

                      
        ($15.75 if she's stacking quarters)

6 0
3 years ago
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