Math / Data & Statistics

QuestionWeights of animals which are modeled by $\mathrm{N}(420 \mathrm{lbs}, 50 \mathrm{lbs}$ .)
6. There is a $94.52 \%$ chance of having the same weight as Jerry the Giraffe. How many standard deviations from the mean is he? a. 1.60 standard deviations b. 1.65 standard deviations light green c. 2.00 standard deviations black d. -1.50 standard deviations yellow grey
7. How much does Jerry weigh? a. 502 lbs purple b. 500 lbs dark red c. 520 lbs dark green d. 345 lbs light brown

Studdy Solution

STEP 1

1. The distribution of animal weights is normal with a mean ( $\mu$ ) of 420 lbs and a standard deviation ( $\sigma$ ) of 50 lbs.
2. The probability of 94.52% corresponds to a specific z-score in a standard normal distribution.

STEP 2

1. Determine the z-score corresponding to a 94.52% probability.
2. Calculate Jerry's weight using the z-score.

STEP 3

To find the z-score corresponding to a 94.52% probability, we look for the z-score where the cumulative distribution function (CDF) is 0.9452.

STEP 4

Using a standard normal distribution table or calculator, find that a probability of 94.52% corresponds to a z-score of approximately 1.60.

STEP 5

To find Jerry's weight, use the formula for a z-score:
$z = \frac{X - \mu}{\sigma}$
where $X$ is Jerry's weight, $\mu = 420$ , and $\sigma = 50$ .

STEP 6

Rearrange the formula to solve for $X$ :
$X = z \cdot \sigma + \mu$
Substitute $z = 1.60$ , $\sigma = 50$ , and $\mu = 420$ :
$X = 1.60 \cdot 50 + 420 = 80 + 420 = 500$
Jerry's weight is:
$\boxed{500 \text{ lbs}}$
The number of standard deviations from the mean is:
$\boxed{1.60}$

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Studdy Solution

STEP 1

1. The distribution of animal weights is normal with a mean ( $\mu$ ) of 420 lbs and a standard deviation ( $\sigma$ ) of 50 lbs.
2. The probability of 94.52% corresponds to a specific z-score in a standard normal distribution.

STEP 2

1. Determine the z-score corresponding to a 94.52% probability.
2. Calculate Jerry's weight using the z-score.

STEP 3

To find the z-score corresponding to a 94.52% probability, we look for the z-score where the cumulative distribution function (CDF) is 0.9452.

STEP 4

Using a standard normal distribution table or calculator, find that a probability of 94.52% corresponds to a z-score of approximately 1.60.

STEP 5

To find Jerry's weight, use the formula for a z-score:
$z = \frac{X - \mu}{\sigma}$
where $X$ is Jerry's weight, $\mu = 420$ , and $\sigma = 50$ .

STEP 6

Rearrange the formula to solve for $X$ :
$X = z \cdot \sigma + \mu$
Substitute $z = 1.60$ , $\sigma = 50$ , and $\mu = 420$ :
$X = 1.60 \cdot 50 + 420 = 80 + 420 = 500$
Jerry's weight is:
$\boxed{500 \text{ lbs}}$
The number of standard deviations from the mean is:
$\boxed{1.60}$

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Studdy Solution

STEP 1

1. The distribution of animal weights is normal with a mean (μ\muμ) of 420 lbs and a standard deviation (σ\sigmaσ) of 50 lbs.2. The probability of 94.52% corresponds to a specific z-score in a standard normal distribution.

STEP 2

1. Determine the z-score corresponding to a 94.52% probability.2. Calculate Jerry's weight using the z-score.

STEP 3

To find the z-score corresponding to a 94.52% probability, we look for the z-score where the cumulative distribution function (CDF) is 0.9452.

STEP 4

Using a standard normal distribution table or calculator, find that a probability of 94.52% corresponds to a z-score of approximately 1.60.

STEP 5

To find Jerry's weight, use the formula for a z-score:z=X−μσ z = \frac{X - \mu}{\sigma} z=σX−μ​where X X X is Jerry's weight, μ=420\mu = 420μ=420, and σ=50\sigma = 50σ=50.

STEP 6

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The distribution of animal weights is normal with a mean ( $\mu$ ) of 420 lbs and a standard deviation ( $\sigma$ ) of 50 lbs.
2. The probability of 94.52% corresponds to a specific z-score in a standard normal distribution.

1. Determine the z-score corresponding to a 94.52% probability.
2. Calculate Jerry's weight using the z-score.

To find Jerry's weight, use the formula for a z-score:
$z = \frac{X - \mu}{\sigma}$
where $X$ is Jerry's weight, $\mu = 420$ , and $\sigma = 50$ .