Which of the following fitness scores is the highest relative score?
1 answer:
Due to the higher z-score, the correct option regarding the highest relative score is:
A score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5.
<h3>What is the z-score formula?</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
The z-score measures how many standard deviations the measure is above or below the mean, hence the higher the z-score, the higher the score X is relative to other scores.
The respective z-scores for this problem are given by:
- (39 - 31)/6.1 = 1.31.
- (1136 - 1080)/67.8 = 0.83.
- (4730 - 3960)/555.5 = 1.39.
Hence the correct option is:
A score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5.
More can be learned about z-scores at brainly.com/question/28096232
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Answer:
a) 0.64
b) 0.21
c) 0.79
Step-by-step explanation:
Percentage of industrial-grade diamonds = 80%
This means, if one diamond is chosen at random, there is 80% chance that it will be of industrial-grade. So,
P(Industrial grade) = 80% = 0.80
Part a)
Probability that 1st diamond is industrial-grade = 0.80
Since, selection of diamonds in independent, the probability that 2nd diamond is also industrial grade = 0.80
The overall probability of both diamonds being industrial-grade will be the product of their individual probabilities, according to the fundamental rule of counting.
So, if two diamonds are chosen at random, the probability that both are industrial grade = 0.80 x 0.80 = (0.80)² = 0.64
Part b)
Following the same logic as we followed in the previous part.
The probability of each of the 7 diamonds being industrial-grade is 0.80, so the probability that all 7 are industrial grade will be:
Probability = 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 = = 0.21
So, if 7 diamonds are chosen at random, the probability that all 7 are industrial grade is 0.21.
Part c)
The event "at least one" is complement of event "none". So, the event "at least one of 7" will be complement of "none of the 7"
If none of the selected diamonds is gem quality, this means all 7 of the diamonds are industrial-grade. So,
The probability that none of the diamonds is gem-quality = The probability that all 7 are industrial-grade = 0.21
So,
The probability that at least one of the 7 selected diamonds is gem-quality = 1 - Probability that none is gem-quality
= 1 - 0.21
= 0.79
Since the probability that atleast one of the 7 randomly selected diamonds is gem-quality is greater than 0.05, it won't be unusual event.