1,241 divided by 43
2 answers:
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Answer:
The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.
Step-by-step explanation:
We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.
The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.
<u><em>Let X = time for this event for boys in secondary school</em></u>
SO, X ~ Normal()
The z-score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = mean time = 460 seconds
= standard deviation = 40 seconds
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
<u>Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;</u>
P(X > x) = 0.10 {where x is the required time which boy need to beat}
P( >
) = 0.10
P(Z > ) = 0.10
<em>So, the critical value of x in the z table which represents the top 10% of the area is given as 1.2816, that is;</em>
<em> </em>
<em> </em> = 460 + 51.264 = <u>511.264 seconds</u>
Hence, the time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.
Answer:
300
Step-by-step explanation:
Students like Vanilla ice cream = 86
Out of 86 Students like chocolate ice cream too = 48
So, No. of students who like only vanilla=86-48 = 38
There were 12 students who did not like vanilla ice cream but liked chocolate ice cream.
There were 2 students who did not like either vanilla ice cream or chocolate ice
Like Vanilla Did not like vanilla Total
Like Chocolate 48 12 60
Did not like chocolate 38 2 40
Total 86 14 100
No. of students who like chocolate out of 100 = 60
Now we are supposed to find the number of students who would like chocolate ice cream when 500 high school students participate in the survey.
Let x be the number of students out of 500 who like chocolate
So, A.T.Q
Hence the number of students who would like chocolate ice cream when 500 high school students participate in the survey is 300.