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Nataliya [291]
3 years ago
15

At winds speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. Wind speeds below 100

0 cm/sec deposit sand, and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large dunes. At a test site, the prevailing direction of the wind did not change noticeably. However, the velocity did change. Sixty wind speed readings gave an average of 1075 cm/sec and based on long term experience the standard deviation for wind speed is 265 cm/sec. Round answers to two decimal places, if necessary(a) Find a 95% confidence interval for the population mean wind speed at this site. (Round your answers to the nearest whole number.)lower limit cm/secupper limit cm/sec
Mathematics
1 answer:
alisha [4.7K]3 years ago
8 0

Answer:

Lower limit = 1007.95 cm/s

Upper limit = 1142.05 cm/s

Step-by-step explanation:

We have to calculate a 95% CI with population's standard deviation known.

The sample is size n=60, with mean M=1075.

The confidence interval can be expressed as:

M-z*\sigma/\sqrt{n} \leq\mu\leq M+z*\sigma/\sqrt{n}

For a 95% CI, the value of z=1.96.

1075-1.96*265/\sqrt{60} \leq\mu\leq 1075+1.96*265/\sqrt{60} \\\\1075-67.05 \leq\mu\leq 1075+67.05\\\\ 1007.95 \leq\mu\leq 1142.05

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Answer: 15/91 which is choice B

=================================================================

There are two methods to find this answer.

Method 1) We have 6 girls and 8+6 = 14 students. The probability of picking a girl is 6/14 = 3/7. After the first girl is chosen, we have 5 girls left out of 14-1 = 13 students overall. The probability of picking another girl (assuming the first selection was a girl) is 5/13. Multiply these probabilities: (3/7)*(5/13) = (3*5)/(7*13) = 15/91

--------------------

Method 2) We can use the nCr combination formula. Order does not matter.

We have nCr = 6 C 2 = 15 ways to pick 2 girls. See the attached image below for the steps (figure 1)

Out of nCr = 14 C 2 = 91 ways to pick 2 students. See the attached image below for the steps (figure 2)

So that's another way to get the answer 15/91.

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