The reading speend second grade students is approximately normal, with a mean of

Question

The reading speend second grade students is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) C. Increasing the sample size increases the probability because sigma decreases as n increases increasing the sample size oecreases the probability because sigma_x increases as n increases. (e) A teacher instituted a new reading program at school After 10 weeks in the program, it was found that the mean reading speed of a random sample of 20 second qr.ide students was 92 1 wpm. What might you conclude based on this result? Select the correct choice and M m the answer box in your choice below.

Explanation / Answer

MEAN = 90

STANDARD DEVIATION = 10

E) WE NEED TO FIND THE PROBABILITY OF EXCEEDING 92.1

AS THE IDTRIBUTIO IS NORMAL WE WILL USE

Z = (X-MEAN)/STANDARD DEVIATION

THEREFORE P(X>92.1) =

) For x = 92.1, z = (92.1 - 90) / 10 = 0.21

Hence P(x > 92.1) = P(z > 0.21) = [total area] - [area to the left of 0.21]

1 - [area to the left of 0.21]

now from the z table we will take the value of z score = 0.21

    = 1 - 0.5832 = 0.4168
THEREFORE OPTION A WITH PROBABILITY 0.4168 IS CORRECT

F) HERE WE WILL USE THE FORMULA =

X = MEAN + ZSCORE* STANDARD DEVIATION

AS THE PROBABILITY GIVEN = 5% = 0.05

WE WILL GET THE Z SCORE FOR 0.05 FROM THE Z TABLE WHICH COMES OUT TO BE = -1.645

THEREFORE X = 90 -1.645*10 = 73.55

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