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MissTica
3 years ago
13

The time (X) to complete a standardized exam is approximately normal with a mean of 70 minutes and standard deviation of 10 minu

tes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?
Mathematics
1 answer:
notka56 [123]3 years ago
5 0

Answer:

77.88 minutes

Step-by-step explanation:

Given that :

Mean (m) = 70

Standard deviation (s) = 10

For 80% of student to complete the exam. In the given time

Using the formula :

Zscore = (X - mean) / standard deviation

80th percentile = 80/100 = 0.8 has a Zscore = 0.7881

0.7881 = (X - 70) /10

0.7881 * 10 = X - 70

7.881 = X - 70

7.881 + 70 = X

77.881 = X

Hence, 77.88 minutes should be given

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Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail inste
Vladimir [108]

Answer:

The value of t test statistics is 5.9028.

We conclude that the true mean is greater than 10 at the .01 level of significance.

Step-by-step explanation:

We are given that a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead.

The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages.

<em />

<em>Let </em>\mu<em> = true mean transmission of pages.</em>

So, Null Hypothesis, H_0 : \mu \leq 10 pages     {means that the true mean is smaller than or equal to 10}

Alternate Hypothesis, H_A : \mu > 10 pages     {means that the true mean is greater than 10}

The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;

                        T.S. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean = 14.44 pages

            s = sample standard deviation = 4.45 pages

            n = sample of fax transmissions = 35

So, <u><em>test statistics</em></u>  =  \frac{14.44-10}{\frac{4.45}{\sqrt{35} } }  ~ t_3_4  

                               =  5.9028

(a) The value of t test statistics is 5.9028.

Now, at 0.01 significance level the z table gives critical values of 2.441 at 34 degree of freedom for right-tailed test.

<em>Since our test statistics is more than the critical values of z as 5.9028 > 2.441, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><em><u>we reject our null hypothesis.</u></em>

Therefore, we conclude that the true mean is greater than 10.

(b) Now, P-value of the test statistics is given by the following formula;

               P-value = P( t_3_4 > 5.9028) = Less than 0.05%    {using t table)

7 0
3 years ago
Plz help :{<br><br> no bad answers plz!!!
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It is not periodic. A periodic dataset is a dataset that repeats the same pattern over time.

7 0
2 years ago
Dunya randomly chooses a number from 1 to 10. What is the probability she
kumpel [21]

Answer: 1/2

Step-by-step explanation:

The numbers that are less than 6 are 1, 2, 3, 4, and 5. Thus simply means that there are 5 numbers that are less than 6.

The probability that she chooses a number less than 6 will then be:

= 5/10

= 1/2

7 0
3 years ago
Julia has correctly answered 35 questions from a test, which is 7/12 of the total. How many questions did the test have?
otez555 [7]

Answer:

There are 60 questions on the test

Step-by-step explanation:

Hope this helps :)

4 0
3 years ago
A stockbroker earns a commission by a flat fee for each transaction as well as a fee per share. On a particular transaction, the
loris [4]
Clearly, alternative B

y = 0.01x + 7.5
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8 0
3 years ago
Read 2 more answers
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