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4 years ago

Equations: -5n=1 n+15= (-10) n/5 = -1/5 n-13= -12 Solutions n= -25 n= -1/5 n= -1 n=1 Match each equation with it's solution

Mathematics

1 answer:

aalyn [17]4 years ago

6 0

Answer:

Step-by-step explanation:

-5n = 1

÷(-5) ÷(-5)

n = -¹/₅

n + 15 = (-10)

-15 -15

n = -25

n/5 = -1/5

×5 ×5

n = -1

n - 13 = -12

+13 +13

n = 1

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4 years ago

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3 years ago

A manufacturer knows that their items have a normally distributed length, with a mean of 13.1 inches, and standard deviation of

Afina-wow [57]

Answer:

0.73% probability that their mean length is less than 11.1 inches

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation, which is also called standard error $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 13.1, \sigma = 4.1, n = 25, s = \frac{4.1}{\sqrt{25}} = 0.82$

What is the probability that their mean length is less than 11.1 inches

This is the pvalue of Z when X = 11.1. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{11.1 - 13.1}{0.82}$

$Z = -2.44$

$Z = -2.44$ has a pvalue of 0.0073.

0.73% probability that their mean length is less than 11.1 inches

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4 years ago

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