Question

It has been said that the age at which a child learns to read is normally distributed. Suppose the average age at which a child learns to read is 5.25 with a standard deviation of 0.49 years. Further, assume that the average class size of 24 may be considered a random sample.

Step 1 of 3:

Describe the sampling distribution that results. Be sure to include all rationales.

Step 2 of 3:

Would it be unusual to find a class with an average reading age of 5.5 years? Why or why not?

Step 3 of 3:

Would it be unusual to find a child who learned to read at age 4.25? Why or why not?

Yes, the probability is 0.0206 which is less than .05

Yes, the probability is 0.0206 which is less than .5

Yes, the probability is effectively 0 which is less than .05

No, the probability is 0.0206 which is greater than .05

Answer 1

Step 1 of 3:

as population is normally distributed. therefore sampling distribution of mean will be  normally distributed. irrespective of sample size.

therefore mean of sampling distribution =5.25

and standard deviation of sampling distribution =0.49/sqrt(24)= 0.100021

Step 2 of 3:

for normal distribution z score =(X-μ)/σ

probability =

P(X>5.5)

=

P(Z>2.5)=

1-P(Z<2.5)=

1-0.9938=

0.0062

as probability 0.0062 is less than 0.05 therefore it is unusual.

Step 3 of 3:

probability =

P(X<4.25)

=

P(Z<-2.04)=

0.0206

Yes, the probability is 0.0206 which is less than .05