In a survey, the IQ scores of 1200 people were recorded - Leaving Cert Mathematics - Question 5 - 2017

According to the Empirical Rule:

• About 68% of the data falls within one standard deviation of the mean (between 85 and 115).
• About 95% of the data falls within two standard deviations of the mean (between 70 and 130).

Thus, the probability that a randomly selected person has an IQ score between 70 and 130 is approximately 95%, or 0.95.

From the previous calculations, we know that approximately 68% of the people fall within one standard deviation of the mean (between 85 and 115).

To find the number of people, we calculate:

$0.68 \times 1200 \approx 816$

Therefore, approximately 816 people surveyed had an IQ score between 85 and 115.

First, calculate the total number of pupils who study chemistry:

• Boys who study chemistry: 6
• Girls who study chemistry: 9 Total = 6 + 9 = 15

Next, calculate the number of pupils who do not study chemistry: Total pupils = 24 Pupils who do not study chemistry = 24 - 15 = 9.

To find the probability that the pupil chosen is either a boy or does not study chemistry, we use the formula:

$P(B \cup C) = P(B) + P(C) - P(B \cap C)$

Where:

• $P(B)$ = Probability of choosing a boy = (\frac{10}{24})
• $P(C)$ = Probability of choosing a pupil who does not study chemistry = (\frac{9}{24})
• $P(B \cap C)$ = Probability of choosing a boy who does not study chemistry = 10 boys - 6 boys studying chemistry = 4 boys not studying chemistry = (\frac{4}{24})

Substituting these values into the formula gives us: $P(B \cup C) = \frac{10}{24} + \frac{9}{24} - \frac{4}{24} = \frac{15}{24}$

Thus, the probability is (\frac{15}{24}) or 62.5%.