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2 years ago

3x - 2(2x - 5) = 2(x + 3) - 8

Mathematics

1 answer:

nataly862011 [7]2 years ago

3 0

Answer:

x = 4

Step-by-step explanation:

Hello!

We can solve for x by expanding the parentheses and isolating x.

<h3>Solve for x</h3>

3x - 2(2x - 5) = 2(x + 3)-8
3x - 4x + 10 = 2x + 6 - 8
-x + 10 = 2x - 2
10 = 3x - 2
12 = 3x
x = 4

The value of x is 4.

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A 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].

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Since in the question only 9 random scores are given, so I am performing the calculation using 9 random scores.

We are given that the scores of bowlers in particular league follow a normal distribution such that the standard deviation of the population is 6.

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Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.

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P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $90.56-1.96 \times {\frac{6}{\sqrt{9} } }$ , $90.56+1.96 \times {\frac{6}{\sqrt{9} } }$ ]

= [86.64 , 94.48]

Therefore, a 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].

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