Assume that adults have IQ scores that are normally distributed with a mean of 1

Question

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Find the probability that a randomly selected adult has an IQ between 90 and 120 (somewhere in the range of normal to bright normal). Find the indicated probability. Round to the nearest thousandth. A sample of 4 different calculators is randomly selected from a group containing 16 that are defective and 30 that have no defects. What is the probability that at least one of the calculators is defective? Identify the null hypothesis, alternative hypothesis, test statistic, P -value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. A supplier of digital memory cards claims that less than 1% of the cards are defective. In a random sample of 600 memory cards, it is found that 3% are defective, but the supplier claims that this is only sample fluctuation. At the 0.01 level of significance, test the supplier's claim that less than 1% are defective.

Explanation / Answer

Q1.

Normal Distribution
Mean ( u ) =100
Standard Deviation ( sd )=15
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 90) = (90-100)/15
= -10/15 = -0.6667
= P ( Z <-0.6667) From Standard Normal Table
= 0.25249
P(X < 120) = (120-100)/15
= 20/15 = 1.3333
= P ( Z <1.3333) From Standard Normal Table
= 0.90879
P(90 < X < 120) = 0.90879-0.25249 = 0.6563                  

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