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Alex73 [517]
3 years ago
13

A fish story: The mean length of one-year-old spotted flounder, in millimeters, is 127 with standard deviation of 22, and the me

an length of two-year-old spotted flounder is 158 with a standard deviation of 23. The distribution of flounder lengths is approximately bell-shaped. Part 1 of 4 (a) Anna caught a one-year-old flounder that was 155 millimeters in length. What is the z-score for this length
Mathematics
1 answer:
pishuonlain [190]3 years ago
4 0

Answer:

The z-score for this length is of 1.27.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

One-year-old flounder:

Mean of 127 with standard deviation of 22, which means that \mu = 127, \sigma = 22

Anna caught a one-year-old flounder that was 155 millimeters in length. What is the z-score for this length

This is Z when X = 155. So

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

Z = \frac{155 - 127}{22}

Z = 1.27

The z-score for this length is of 1.27.

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mario62 [17]

Answer:

The experimental probability of throwing a five is 0.087.

Step-by-step explanation:

Given:

Number of trials (n) = 100

Number of times 5 appears (x) = 14

Let the event of occurrence of 5 be success and the probability represented by 'p'. So, all the other numbers occurrence is failure and its probability is represented as 'q'.

Probability of success is given as:

p=\frac{Number\ of\ favorable\ events}{Total\ number\ of\ outcomes}

Favorable event is occurrence of 5. So, its number is 1 as there is only one 5 in the die. Total outcomes are 6 as there are six numbers. So,

p=\frac{1}{6}

Now, probability of failure is given by the formula:

q=1-p=1-\frac{1}{6}=\frac{5}{6}

Now in order to find the experimental probability of 14 successes out of 100 trials, we apply Bernoulli's theorem which is given as:

P(x) = ^nC_xp^xq^{n-x}

Plug in all the given values and find the probability of 14 successes. This gives,

P(x=14)=^{100}C_{14}(\frac{1}{6})^{14}(\frac{5}{6})^{100-14}\\\\P(x=14)=0.087

Therefore, the experimental probability of throwing a five is 0.087.

8 0
3 years ago
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andrew-mc [135]

A

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Answer:

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Step-by-step explanation:

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<em />

In the given figure

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