The reading speed of 2nd grade students is approximately a mean words a minute a

Question

The reading speed of 2nd grade students is approximately a mean words a minute and a standard with deviation of words per minute of 9o calculator. below address the following questions. Show keystrokes if using a) What is the probability that a randomly selected student will read more than b) words per Give appropriate notation and interpret the result. What is the probability that random of grade students appropriate mean reading rate of more than 95 words per minute? the notation and interpret the c) What is the probability that a random sample of second grade students results in a mean reading rate of more than 95 words per minute? Give the d) appropriate notation and interpret the result. have on the probability? effect does the increasing the ample sizes Provide an explanation for this result?

Explanation / Answer

Solution of question 27:

The reading speed of second grade students is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm.

a) What is the probability a randomly selected student will read more than 95 words per minute?

Convert to a z score using the formula z = (x mean)/sd

Z = (95 90)/10 = 0.5

P(X > 95) = P(Z > 0.5) = 1 P(Z < 0.5) = 0.3085 (answer)

b) What is the probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute?

Convert to a z score using the formula z = (xbar mean)/(sd/sqrt n)

Z = (95 90)/(10/sqrt 12) = 1.73

P(Xbar > 95) = P(Z > 1.73) = 1 P(Z < 1.73) = 0.0418 (answer)

c) What is the probability that a random sample of 24 second grade students results in a mean reading rate of more than 95 words per minute?

Convert to a z score using the formula z = (xbar mean)/(sd/sqrt n)

Z = (95 90)/(10/sqrt 24) = 2.45

P(Xbar > 95) = P(Z > 2.45) = 1 P(Z < 2.45) = 0.0071 (answer)

d) What effect does increasing the sample size have on the probability? Provide an explanation for this result.

Increasing the sample size decreases the probability that a sample mean is going to be greater than 95. This is because as the sample size increases, the sample means get closer to the population mean of 90.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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