Question

I need what to put on the TI-84 calculator and verify that all conditions of the Central Limit Theorem have been met. Answer is next to the question on the bracket.

Note: Before answering the following questions, make sure to verify that all conditions of the Central Limit Theorem have been met.
7.2.1 On an average day in 2013, 83% of women and 65% of men spent some time doing household activities such as housework, cooking, lawn care, and financial or other household management. Source: American Time Use Survey, BLS.gov.

a. If 500 men are randomly selected, what is the probability that at least 70% of them spent some time doing household activities on an average day? (0.0095)
b. If 500 women are randomly selected, what is the probability that at least 85% of them spent some time doing household activities on an average day? (0.1169)
c. If 300 men were randomly selected, what is the probability that at least 64% of them spent some time doing household activities on an average day? (0.6417)
d. If 300 women were randomly selected, what is the probability that at least 75% of them spent some time doing household activities on an average day? (0.9999)
e. Would it be an unusual event if a random sample of 1,200 men was conducted and more than 67% of them spent some time doing household activities on an average day? Explain and justify your answer.

Answer 1

Conditions of the central limit theorem:

n*p 10 and

n(1-p)   10

e.g.

A.

np = 500*0.65 = 325 10 and,

n(1-p) = 175 10

Thus, central limit condition is satisfied and we can use normal apporximation as folows:

Ti-84 Formula:

normalcdf (lower bound, upper bound, mean, standard deviation)

normalcdf(0.7, 1 EE 99, 0.65, 0.0213) ; where 1 EE 99 represents infinity

B.

normalcdf(0.85, 1 EE 99, 0.83, 0.0168) ; where 1 EE 99 represents infinity

C.

normalcdf(0.64, 1 EE 99, 0.65, 0.0275)

D.

normalcdf(0.75, 1 EE 99, 0.83, 0.0217)

E.

normalcdf(0.67, 1 EE 99, 0.65, 0.0138)

= 0.0732 > 0.05 i.e. it is not an unusual event.

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