I need help desperately

One environmental group did a study of recycling habits in a California community. It found that 75% of the aluminum cans sold i

AysviL [449]

Answer:

a

$P( \^ p > 0.775 ) = 0.12798$

b

$P( 0.6718 < p < 0.775 ) =0.87183$

Step-by-step explanation:

From the question we are told that

The population proportion is $p = 0.75$

Considering question a

The sample size is $n = 387$

Generally the standard deviation of this sampling distribution is

$\sigma = \sqrt{ \frac{p(1 - p)}{ n } }$

=> $\sigma = \sqrt{ \frac{0.75(1 - 0.75)}{ 387 } }$

=> $\sigma = 0.022$

The sample proportion of cans that are recycled is

$\^ p = \frac{ 300}{387 }$

=> $\^ p = 0.775$

Generally the probability that 300 or more will be recycled is mathematically represented as

$P( \^ p > 0.775 ) = P( \frac{\^ p - p }{ \sigma } > \frac{0.775 - 0.75 }{ 0.022} )$

$\frac{\^ p - p }{\sigma } = Z (The \ standardized \ value\ of \ \^ p )$

$P( \^ p > 0.775 ) = P( Z > 1.136 )$

From the z table the area under the normal curve to the left corresponding to 1.591 is

$P( Z > 1.136) = 0.12798$

=> $P( \^ p > 0.775 ) = 0.12798$

Considering question b

Generally the lower limit of sample proportion of cans that are recycled is

$\^ p_1 = \frac{ 260 }{387 }$

=> $\^ p_1 = 0.6718$

Generally the upper limit of sample proportion of cans that are recycled is

$\^ p_2 = \frac{ 300}{387 }$

=> $\^ p_2 = 0.775$

Generally probability that between 260 and 300 will be recycled is mathematically represented as

$P( 0.6718 < p < 0.775 ) = P( \frac{0.6718 - 0.75 }{ 0.022}< \frac{\^ p - p }{ \sigma }$

=> $P( 0.6718 < p < 0.775 ) = P( -3.55 < Z < 1.136 )$

=> $P( 0.6718 < p < 0.775 ) = P(Z < 1.136 ) - P( Z < -3.55 )$

From the z table the area under the normal curve to the left corresponding to 1.136 and -3.55 is

$P( Z < -3.55 ) = 0.00019262$

and

$P(Z < 1.136 ) = 0.87202$

So

$P( 0.6718 < p < 0.775 ) = 0.87202- 0.00019262$

=> $P( 0.6718 < p < 0.775 ) =0.87183$

4 0

2 years ago

The profit of a company receives is given by the expression 0.15(855p - 315) where p is the number of problems sold. Rewrite thi

Goryan [66]

The profit for 25 products sold and 150 products sold are 3159 and 19190.25 respectively.

Explanation

The profit of a company receives is given by the expression: $0.15(855p - 315)$

Simplifying this expression using distributive property, we will get .....

$0.15(855p - 315) \\ \\ = (0.15*855p)-(0.15*315)\\ \\ =128.25p-47.25$

So, the simplified expression for profit will be: $128.25p-47.25$

As $p$ represents the number of products sold, so for finding the profit for 25 products sold and 150 products sold, we need plug $p=25$ and $p=150$ separately into the above expression.

For $p=25$ , Profit $=128.25(25)-47.25 = 3206.25-47.25= 3159$

For $p=150$ , Profit $=128.25(150)-47.25 = 19237.50-47.25= 19190.25$

5 0

2 years ago

Factorize 1-(3x-1)^2

solniwko [45]

Step-by-step explanation:

(1+3x-1)×{1-(3x-1)}

=3x.(1-3x+1)

=3x.3x

=9x^2.

6 0

2 years ago

HELP ASAP

AlekseyPX

We’ll subtract the exponent in the denominator from the exponent in the numerator, keeping the base the same. Cant be simplified, because the base of the expression in the numerator is y and the base of the expression in the denominator is x.

4 0

2 years ago

A catering service offers 5 appetizers,4 main courses, and 8 desserts. A customer is to select 4 appetizers,2 main courses,and 3

Alisiya [41]

Answer:

468 ways

Step-by-step explanation:

Given: A catering service offers 5 appetizers, 4 main courses, and 8 desserts

To find: number of ways a customer is to select 4 appetizers, 2 main courses,and 3 desserts.

Solution:

A permutation is an arrangement of elements such that order of elements matters and repetition is not allowed.

Number of appetizers = 5

Number of main courses = 4

Number of desserts = 8

Number of ways of choosing k terms from n terms = $nPk=\frac{n!}{(n-k)!}$

Number of ways a customer is to select 4 appetizers, 2 main courses,and 3 desserts = $5P4+4P2+8P3$

$=\frac{5!}{(5-4)!}+\frac{4!}{(4-2)!}+\frac{81}{(8-3)!}\\=5!+\frac{4!}{2!}+\frac{8!}{5!}\\=5!+(4\times 3)+(8\times 7\times 6)\\=120+12+336\\=468$

So, this can be done in 468 ways.

7 0

2 years ago