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3 years ago

7

john can play 12songs on the guitar and he learns 1 new song each week. Aiden can play 4 songs but he learns 2 each week. How ma

ny weeks will it be before aiden knows as many songs as john?

1 answer:

Margarita [4]3 years ago

4 0

4 weeks if John doesn't learn anymore new songs but if he continues to learn one new song per week by week 8 John and Aiden will both be at 20 songs

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Answer:

(22.12, 27.48)

Step-by-step explanation:

Given : Significance level : $\alpha: 1-0.95=0.05$

Sample size : n= 8 , which is a small sample (n<30), so we use t-test.

Critical values using t-distribution: $t_{n-1,\alpha/2}=t_{7,0.025}=2.365$

Sample mean : $\overline{x}=24.8\text{ hours}$

Standard deviation : $\sigma=3.2\text{ hours}$

The confidence interval for population means is given by :-

$\overline{x}\pm t_{n-1,\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

i.e. $24.8\pm(2.365)\dfrac{3.2}{\sqrt{8}}$

$24.8\pm2.67569206001\\\\\approx24.8\pm2.68\\\\=(24.8-2.68, 24.8+2.68)=(22.12, 27.48)$

Hence, the 95% confidence interval, assuming the times are normally distributed.= (22.12, 27.48)

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Step-by-step explanation:

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