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3 years ago

What is the average of all integers from 11 to 35

Mathematics

2 answers:

horsena [70]3 years ago

5 0

24 becuase add the two together then divide by two

Lena [83]3 years ago

5 0

1st let's calculate the sum from 1 to 35:

it's an arithmetic progression with first term a = 11, last term = 35 and the number of term n = 25

s= (11+35)25/2 = 575

Average = 575/25 = 23

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A survey asked, "How many tattoos do you currently have on your body?" Of the males surveyed, responded that they had at leas

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Complete Question

The complete question is shown on the first uploaded image

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The 95% interval for $p_1 - p_2$ is $-0.0171 ,0.0411$

Option A is correct

Step-by-step explanation:

From the question we are told that

The sample size of male is $n_1 = 1211$

The number of males that said they have at least one tattoo is $r = 182$

The sample size of female is $n_2 = 1041$

The number of females that said they have at least one tattoo is $k = 144$

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$\r p_1 = \frac{r}{ n_1}$

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$\r p_1 = 0.1503$

Generally the sample proportion of female is

$\r p_2 = \frac{k}{ n_2}$

substituting values

$\r p_2 = \frac{ 144}{1041}$

$\r p_2 = 0.1383$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha =100-95$

$\alpha =5\%$

$\alpha =0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table , the value is

$Z_\frac{\alpha }{2} = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p_1 (1- \r p_1)}{n_1} + \frac{\r p_2 (1- \r p_2)}{n_2} }$

substituting values

$E = 1.96 * \sqrt{\frac{ 0.1503 (1- 0.1503)}{1211} + \frac{0.1383 (1- 0.1383)}{1041} }$

$E = 0.0291$

The 95% confidence interval is mathematically represented as

$(\r p_1 - \r p_2 ) - E < p_1-p_2 < (\r p_1 - \r p_2 ) + E$

substituting values

$(0.1503- 0.1383 ) - 0.0291 < p_1-p_2 < (0.1503- 0.1383 ) + 0.0291$

$-0.0171 < p_1-p_2 < 0.0411$

So the interpretation is that there is 95% confidence that the difference of the proportion is in the interval .So conclude that there is insufficient evidence of a significant difference in the proportion of male and female that have at least one tattoo

This because the difference in proportion is less than $\alpha$

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