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Allushta [10]
3 years ago
12

Grant is trying to make money to help pay for college by taking a job with Brian’s bike taxis if Baltimore. He has an agreement

with Brian to rent the bike for $35.00 a night. He charges customers $3.75 for every mile he transports them. If grant needs to make at least $15.00 a day, how many miles would he need to ride?
Mathematics
1 answer:
alexandr402 [8]3 years ago
7 0

Grant needs to ride at least 13.33 miles to male at least $ 15.00 a day

<em><u>Solution:</u></em>

Given that Grant has an agreement with Brian to rent the bike for $35.00 a night

He charges customers $3.75 for every mile he transports them

Grant needs to make at least $15.00 a day

To find: miles needed to ride

From given question, He charges customers $3.75 for every mile he transports them

So if he transports for "x" miles he would get,

\$ 3.75 \times x = \$ 3.75x

So the profit he gets is $ 3.75 and initial cost invested to rent bike is $ 35. Also, Grant needs to make at least $15.00 a day

So we can frame a inequality as:

3.75x - 35 \geq 15\\\\3.75x\geq 35 + 15\\\\3.75x\geq 50\\\\x \geq 13.33

So he needs to ride atleast 13.33 miles to male atleast $ 15.00 a day

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Answer:

z=\frac{p_{M}-p_{W}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{M}}+\frac{1}{n_{W}})}}   (1)

z=\frac{0.34848-0.34782}{\sqrt{0.34831(1-0.34831)(\frac{1}{66}+\frac{1}{23})}}=0.0057  

p_v =P(Z>0.0057)=0.4977  

The p value is a very high value and using the significance level \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the percent of men who enjoy shopping for electronic equipment is NOT significantly higher than the percent of women who enjoy shopping for electronic equipment.  

Step-by-step explanation:

1) Data given and notation  

X_{M}=23 represent the number of men that said they enjoyed the activity of Saturday afternoon shopping

X_{W}=8 represent the number of women that said they enjoyed the activity of Saturday afternoon shopping

n_{M}=66 sample of male selected

n_{W}=23 sample of demale selected

p_{M}=\frac{23}{66}=0.34848 represent the proportion of men that said they enjoyed the activity of Saturday afternoon shopping

p_{W}=\frac{8}{23}=0.34782 represent the proportion of women with red/green color blindness  

z would represent the statistic (variable of interest)  

p_v represent the value for the test (variable of interest)

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the percent of men who enjoy shopping for electronic equipment is higher than the percent of women who enjoy shopping for electronic equipment , the system of hypothesis would be:  

Null hypothesis:p_{M} \leq p_{W}  

Alternative hypothesis:p_{M} > p_{W}  

We need to apply a z test to compare proportions, and the statistic is given by:  

z=\frac{p_{M}-p_{W}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{M}}+\frac{1}{n_{W}})}}   (1)

Where \hat p=\frac{X_{M}+X_{W}}{n_{M}+n_{W}}=\frac{23+8}{66+23}=0.34831

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:  

z=\frac{0.34848-0.34782}{\sqrt{0.34831(1-0.34831)(\frac{1}{66}+\frac{1}{23})}}=0.0057  

4) Statistical decision

Using the significance level provided \alpha=0.05, the next step would be calculate the p value for this test.  

Since is a one side right tail test the p value would be:  

p_v =P(Z>0.0057)=0.4977  

So the p value is a very high value and using the significance level \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the percent of men who enjoy shopping for electronic equipment is NOT significantly higher than the percent of women who enjoy shopping for electronic equipment.  

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Answer:

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Step-by-step explanation:

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