The scores of high school seniors on the ACT college entrance examination in a r

Question

The scores of high school seniors on the ACT college entrance examination in a recent year had mean u 22.3 and standard deviation 5.2. The distribution of scores is only roughly Normal. What is the approximate probabilty that the mean score E 4 students is 27 or higher? (use table A) of O 0.0344 Step 4: The scores of high school seniors on the ACT college entrance examination in a recent year had mean 223 and standard deviation 5.2, The distribution of scores is only roughly Normal. which of your two Normal probability calculations in (a) and (c) is more accurate? Why? O cannot tell. Since

Explanation / Answer

Solution:

Step 3: option C) 0.0344

the approximate probability that the mean score x of 4 students is 27 or higher   
With = 22.3 and = 5.2, converting to a z-score gives
= 5.2 /4 = 2.6   
Find P( x > 27 )
P( ( x - ) / > ( 27 - 22.3 ) / 2.6)
= P ( Z>1.807692 )
= 1P ( Z<1.807692 )
= 10.9649
= 0.0351 (approximate value)

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