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valkas [14]
3 years ago
7

Listed below are speeds (mi/h) measured from southbound traffic on I-280 near Cupertino, California (based on data from SigAlert

). This simple random sample was obtained at 3:30 pm on a weekday. Use the sample data to construct a 95% confidence interval estimate of the population standard deviation. 62 61 61 57 61 54 59 58 59 69 60 67A.) 4.7 mi/h< <5.6 mi/h
b.) 2.9 mi/h< <6.9 mi/h

c.) 3.1 mi/h< <8.5 mi/h

d.) 1.6 mi/h< <4.9 mi/h

e.) 5.4 mi/h< <9.2 mi/h
Mathematics
1 answer:
adell [148]3 years ago
5 0

Answer:

Option (B) is the correct answer to the following question.

Step-by-step explanation:

Step-1: We have to find the Mean of the series.

The series is Given in the question 62 61 61 57 61 54 59 58 59 69 60 67.

Mean(\overline{x})=\frac{62+61+61+57+61+54+59+58+59+69+60+67}{12} = 60.67

Step-2: We have to find the Standard Deviation.

Let Standard Deviation be x.

Formula of Standard Deviation is: s= \sqrt{\frac{\sum(x_{i}+\overline{x})}{n-1}}

Put value in formula of Standard Deviation,

s= \sqrt{\frac{(62+60.67)^{2}+(61+60.67)^{2}+(61+60.67)^{2}+(57+60.67)^{2}+....(67+60.67)^{2}}{n-1}} = 40.75

Step-3: Then, we have to find the critical value by chi-square.

X_{1-\alpha/2}^{2}=3.82

X_{1-\alpha/2}^{2}=21.92

Then, find the confidence interval which is 95%.

\sqrt{\frac{(n-1).s^2}{X_{\alpha/2}^{2}} } = \sqrt{\frac{12-1}{21.92}.(4.075)^2 }\approx2.8868 \\ i.e 2.9

\sqrt{\frac{(n-1).s^2}{X_{\alpha/2}^{2}} } = \sqrt{\frac{12-1}{3.816}.(4.075)^2 }\approx6.9188 \\ i.e 6.9

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b. The ball has to travel about 314.24 yards

Step-by-step explanation:

* Let us explain how to solve the problem

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a.

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- We need to find the percent of Spieth's drives travel at least

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∵ The mean μ = 304 yards

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∵ The distance x = 290

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* <em>About 96% of Spieth's drives travel at least 290 yards</em>

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  onto the green if he hits the ball a distance  in the top 10% of all

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- Let us find the z-score from the normal distribution table for the 10%

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∵ The area which equivalent to 0.9 ≅ 0.89973

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∵ z-score = (x - μ)/σ

∴ 1.28 = \frac{x-304}{8}

- Multiply both sides by 8

∴ 10.24 = x - 304

- Add 304 for both sides

∴ x = 314.24 yards

* <em>The ball has to travel about 314.24 yards</em>

8 0
3 years ago
a recipe calls for 3 cups of flour and 2 cups of sugar if you only have 2.5 cups of sugar to keep it proportional how much sugar
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Answer:

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Answer: 2.4 cups of sugar

Hope this helped!! :)

Brainliest?!?!

Stay safe and have a wonderful day/night/afternoon!!!

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