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Zielflug [23.3K]
3 years ago
6

A simple random sample of 20 days in which Parsnip ate seeds was selected, and the mean amount of time it took him to eat the se

eds was 14.5 seconds with a standard deviation of 3.98 seconds. An independent simple random sample of 17 days in which Parsnip ate pellets was selected, and the mean amount of time it took him to eat the pellets was 13.9 seconds with a standard deviation of 4.03 seconds. If appropriate, use this information to calculate and interpret a 90% confidence interval for the difference in the mean amount of time it takes Parsnip to eat seeds and the mean amount of time it takes Parsnip to eat pellets.
Mathematics
1 answer:
bearhunter [10]3 years ago
5 0

Answer:

(14.5-13.9) -1.69 \sqrt{\frac{3.98^2}{20}+ \frac{4.03^2}{17}} = -1.63

(14.5-13.9) +1.69 \sqrt{\frac{3.98^2}{20}+ \frac{4.03^2}{17}} = 2.83

And the confidence interval for this case -1.63 \leq \mu_1 -\mu_2 \leq 2.83

Step-by-step explanation:

We know the following info from the problem

\bar X_1 = 14.5 sample mean for the group 1

s_1 = 3.98 the standard deviation for the group 1

n_1= 20 the sample size for group 1

\bar X_2 = 13.9 sample mean for the group 2

s_1 = 4.03 the standard deviation for the group 2

n_2= 17 the sample size for group 2

We have all the conditions satisifed since we have random samples.

We want to construct a confidence interval for the true difference of means and the correct formula for this case is:

(\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}

The degrees of freedom are given :

df = n_1 +n_2- 2 = 20+17-2=35

The confidence level is 0.9 or 90% and the significance level is \alpha=1-0.9=0.1 and \alpha/2 = 0.05 and the critical value for this case is:

t_{\alpha/2} = 1.69

And replacing the info given we got:

(14.5-13.9) -1.69 \sqrt{\frac{3.98^2}{20}+ \frac{4.03^2}{17}} = -1.63

(14.5-13.9) +1.69 \sqrt{\frac{3.98^2}{20}+ \frac{4.03^2}{17}} = 2.83

And the confidence interval for this case -1.63 \leq \mu_1 -\mu_2 \leq 2.83

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Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability,
Maurinko [17]

Answer:

0.1662 = 16.62% probability that exactly 2 will stay with the same company for more than five years

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they stay for the same company for more than five years, or they do not. Graduates are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

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Sample of 11 college graduates:

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The tolerance means that the answer is rounded to four decimal places.

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4 0
3 years ago
Después de 15 meses de haber prestado un capital al 5% de rédito, tengo que pagar de interés Q468.75. ¿Qué capital se ha prestad
Aleonysh [2.5K]

The capital borrowed, or the principal when the interest was Q468.75 is <u>Q7500</u>.

The principal P, amount borrowed, at a certain rate of interest R%, for  a time of T years, giving an interest of I, can be calculated using the formula:

P = (I * 100)/(R * T).

In the question, we are asked to find the capital borrowed, that is, the principal, when the user pays Q468.75 after 15 months at 5% of income.

Thus, Interest (I) = Q468.75, rate of interest (R) = 5%, and time (T) = 15 months = 15/12 years = 1.25 years.

Thus, the principal P, can be calculated by substituting the values in the formula: P = (I * 100)/(R * T).

P = (468.75*100)/(5*1.25),

or, P = 46875/6.25,

or, P = 7500.

Thus, the capital borrowed, or the principal when the interest was Q468.75 is <u>Q7500</u>.

The provided question is in Spanish. The question in English is:

"After 15 months of having borrowed capital at 5% of income, I have to pay Q468.75 in interest. What capital has been borrowed?"

Learn more about Interest at

brainly.com/question/25793394

#SPJ1

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