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3 years ago

Jeremy’s password is the combination of letters and numbers shown below.

Mathematics

1 answer:

alisha [4.7K]3 years ago

7 0

Answer: Odd:Even --> 3:2 and Vowels:Letters --> 2:4

Step-by-step explanation:

27RQA58E3

Odd #s: 7, 5, & 3 --> 3

Even #s: 2 & 8 --> 2

Even:Odd --> 3:2

Vowels: A & E --> 2

Letters: R, Q, A, & E --> 4

Vowels:Letters --> 2:4

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Answer:

(a) The 95% confidence interval for the population proportion of US adults for whom math was their most favorite subject is (0.204, 0.256).

(b) The 95% confidence interval for the population proportion of US adults for whom math was their least favorite subject is (0.34, 0.40).

Step-by-step explanation:

The questions are:

(a) Construct and interpret a 95% confidence interval for the proportion of US adults for whom math was their most favorite subject.

(b) Construct and interpret a 95% confidence interval for the proportion of US adults for whom math was their least favorite subject. Solution:

(a)

The 95% confidence interval for the population proportion is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Th information provided is:

n = 1000

Number of US adults for whom math was their most favorite subject

= X

= 230

Compute the sample proportion of US adults for whom math was their most favorite subject as follows:

$\hat p=\frac{230}{1000}=0.23$

The critical value of z for 95% confidence interval is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Compute the 95% confidence interval for the population proportion of US adults for whom math was their most favorite subject as follows:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=0.23\pm 1.96\sqrt{\frac{0.23(1-0.23)}{1000}}\\=0.23\pm 0.0261\\=(0.2039, 0.2561)\\\approx (0.204, 0.256)$

Thus, the 95% confidence interval for the population proportion of US adults for whom math was their most favorite subject is (0.204, 0.256).

(b)

The 95% confidence interval for the population proportion is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Th information provided is:

n = 1000

Number of US adults for whom math was their least favorite subject

= X

= 370

Compute the sample proportion of US adults for whom math was their least favorite subject as follows:

$\hat p=\frac{370}{1000}=0.37$

The critical value of z for 95% confidence interval is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Compute the 95% confidence interval for the population proportion of US adults for whom math was their least favorite subject as follows:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=0.37\pm 1.96\sqrt{\frac{0.37(1-0.37)}{1000}}\\=0.37\pm 0.0299\\=(0.3401, 0.3999)\\\approx (0.34, 0.40)$

Thus, the 95% confidence interval for the population proportion of US adults for whom math was their least favorite subject is (0.34, 0.40).

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