Scores on the Stanford-Binet Intelligence Test are normally distributed with mea

Question

Scores on the Stanford-Binet Intelligence Test are normally distributed with mean mu = 100 and standard deviation sigma = 16. (a) Determine the 90^th percentile of IQs. (b) Determine the IQs that make up the middle 70% of IQs. The reading speed of 6^th grades is approximately normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute. (a) What is the reading speed of a 6^th grader whose reading speed is at the 95^th percentile? (b) A school psychologist wants to determine reading rates for unusual students (both slow and fast). What are the cutoff points for the unusual readers?

Explanation / Answer

we are given that mean = 100 and sd = 16

a) we need to find 90th percentile

so we shall use z tables to first check what the z value is for 0.90 , we see the value is 1.28

now we must use the fomrula

Z = (X-Mean)/SD, so

1.28 = (X-100)/ 16, solving for X we get

X = 100+ 1.28*16 = 120.48

b) middle 70% means that 15% on the left and 15% on the right are excluded from the area of the normal curve

so we must find 15% to 85%

so z15 = -1.036

z85 = 1.036

so we use z score again 1.036 = (X-100)/16

X = 100+1.036*16= 116.57

and the other one would be

-1.036 = (X-100)/16

X = 100-1.036*16= 83.42 , so the 2 scores are 83.42 and 116.57

Please note that we can answer only 1 full question at a time , as per the answering guidelines

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.