Name: (1) Find az value such that 20% of the area under the standard normal eam

Question

Name: (1) Find az value such that 20% of the area under the standard normal eam lis to the left of (2) Find a:value such that 20% of the area under the standard normal curve lies to the right of 2. (3) Find al and a2 such that the middle 20% of all area under the standard normal curve lies between 2 and (4) The mean value of X for a given population is ? 2.52 and ?-0.23. Find the X value that ha a-score of 1.28. (5) Suppose that the scores on specific standardized test are normally distributed with mean ?-1, 200 130. and standard deviation ? (a) If a random sample of 16 test takers is selected, what is the probability that their mean score will be lower than 1,1007 (b) If a random sample of 16 test takers is selected, what is the probability that their mean score will be higher than 1,200? (c) If a random sample of 16 test takers is selected, what is the probability that their mean score will be between 1,100 and 1,300? (d) A local college only accepts applicants that have scored in the top 20% on the test, what is the lowest score someone can get and still be admitted in to the college? (e) A local college only accepts applicants with scores in the lowest 10% of the distribution. What Is the highest score that someone can get and still be admitted in to the college? f) A local college only accepts applicants with scores in the middle 30% of the distribution is the lowest and highest score a person can get and still be admitted to the college? what

Explanation / Answer

Solution :

Usin g standard normal table,

1) P(Z < z) = 20%

P(Z < z) = 0.20

P(Z < -0.84) = 0.20

z = -0.84

2) P(Z > z) = 0.20

1 - P(Z < z) = 0.20

P(Z < z) = 1 - 0.20 = 0.80

P(Z < 0.84) = 0.20

z = 0.84

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