The is a normal distribution with the parameters of population mean equal to 0 a

Question

The is a normal distribution with the parameters of population mean equal to 0 and the population standard deviation equal to 1. Poisson Distribution Binomial Distribution Hypergeometric Distribution Standard Normal Distribution None Assume the z-scores of the bone mineral density test values are normally distributed with a mean of 0 and a standard deviation of 1 Consider that bone density test reading between -1.00 and 2.50 reveals that the subject has osteopenia (or some bone loss). Find the probability that a randomly selected subject has a reading between -1.00 and -2.50. 0.0062 0.1587 0.1649 0.1525 None When designing an environment, one common criterion is to use a design that accommodates 95% of the population. What aircraft ceiling height will allow 95% of men to stand without bumping their heads? That is, find the 95^th percentile of heights of men. Assume that heights of men are normally distributed with a mean of 69.5 in. and a standard deviation of 2.4 in. 69.5 in. 76.7 in. 82.4 in. 73.4 in. none In 431 NFL football games that went to overtime, the teams that won the coin toss went on to win 235 of those games. If the coin-toss method is fair, we expect that the teams winning the coin would win about 50% of the games, so we expect about 215.5 wins in 431 overtime games. Assuming that there is aO.5 probability of winning a game after winning the coin toss, find the probability of getting at least 235 winning games among the 431 teams that won the coin toss. That is, given n = 431 and p = 0.5, find the probability of at least 235 wins. 0.3803 0.0035 0.9664 0.0336 None

Explanation / Answer

1.

By definition,

OPTION D: Standard Normal Distribution [ANSWER]

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2.

z1 = lower z score =    -2.5      
z2 = upper z score =     -1      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.006209665      
P(z < z2) =    0.158655254      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.1525 [ANSWER, D]

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3.

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.95      
          
Then, using table or technology,          
          
z =    1.644853627      
          
As x = u + z * s,          
          
where          
          
u = mean =    69.5      
z = the critical z score =    1.644853627      
s = standard deviation =    2.4      
          
Then          
          
x = critical value =    73.4476487   [ANSWER, D]

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4.

We first get the z score for the critical value:          
          
x = critical value =    234.5      
u = mean = np =    215.5      
          
s = standard deviation = sqrt(np(1-p)) =    10.38026975      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    1.830395593      
          
Thus, the right tailed area is          
          
P(z >   1.830395593   ) =    0.033595403 [ANSWER, D]
  

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