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just olya [345]
2 years ago
12

Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with μ=10

6 and σ=15. (a) What proportion of children aged 13 to 15 years old have scores on this test above 92 ? (Reminder: proportions are between 0 and 1 - don't put in percentages!)
Mathematics
1 answer:
Tju [1.3M]2 years ago
4 0

Answer: 0.8238

Step-by-step explanation:

Given : Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with \mu=106 and \sigma=15.

Let x denotes the scores on a certain intelligence test for children between ages 13 and 15 years.

Then, the proportion of children aged 13 to 15 years old have scores on this test above 92 will be :-

P(x>92)=1-P(x\leq92)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{92-106}{15})\\\\=1-P(z\leq })\\\\=1-P(z\leq-0.93)=1-(1-P(z\leq0.93))\ \ [\because\ P(Z\leq -z)=1-P(Z\leq z)]\\\\=P(z\leq0.93)=0.8238\ \ [\text{By using z-value table.}]

Hence, the proportion of children aged 13 to 15 years old have scores on this test above 92 = 0.8238

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