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Sindrei [870]
3 years ago
6

A data set has a normal distribution with a mean of 47 and a standard deviation of 4.6. Use this information to scale the horizo

ntal axis with the mean of this distribution and values at 1, 2, and 3 standard deviations above and below the mean.
Mathematics
1 answer:
gulaghasi [49]3 years ago
8 0

Horizontal axis with 1, 2, and 3 standard deviations above the mean are 51.6, 56.2, 60.8

Horizontal axis with 1, 2, and 3 standard deviations below the mean are 42.4, 37.8, 33.2

<u>Step-by-step explanation:</u>

A data set has a normal distribution with a mean of 47 and a standard deviation of 4.6

  • Mean, M ⇒ 47
  • Standard deviation ⇒ 4.6

From this information, you have to scale the horizontal axis with the mean of this distribution and values at 1, 2, and 3 standard deviations above and below the mean.

Horizontal axis with 1, 2, and 3 standard deviations above the mean :

1 standard deviation above the mean ⇒ M + SD

⇒ 47 + 4.6 = 51.6

2 standard deviations above the mean ⇒ M + 2SD

⇒ 47 + (2 × 4.6) = 56.2

3 standard deviations above the mean ⇒ M + 3SD

⇒ 47 + (3 × 4.6) = 60.8

Horizontal axis with 1, 2, and 3 standard deviations below the mean :

1 standard deviation below the mean ⇒ M - SD

⇒ 47 - 4.6 = 42.4

2 standard deviations below the mean ⇒ M - 2SD

⇒ 47 - (2 × 4.6) = 37.8

3 standard deviations below the mean ⇒ M - 3SD

⇒ 47 - (3 × 4.6) = 33.2

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<em><u>Solution:</u></em>

Given that,

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Also for every 2 dimes there are 5 quarters

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Let us first find the ratio of nickles to dimes to quarters

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So,

nickel : dime : quarter = \frac{2}{3}dime : dime : \frac{5}{2}dime\\\\nickel : dime : quarter = \frac{2}{3} : 1 : \frac{5}{2}\\\\nickel : dime : quarter = 4 : 6 : 15

Thus nickel : dime : quarters = 4 : 6 : 15

Now, let the number of nickel be 4x

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From given question,

There are 500 coins in all.

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number of quarters = 15x = 15(20) = 300

Thus there are 80 nickels and 120 dimes and 300 quarters in piggy bank    

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