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# Help!!Noraml Distribution

1. The statistics department at a local university notes that the English scores of

high school seniors applying admission into their program are normally distributed with mean 610 marks and standard deviation 50 marks.

(a) If 15%students gets grade A, 25% students gets grade B, 40% students gets

grade C, and the 20% gets grade D. What are the minimium criteria to get A and B respectively?

(b)what are the mean and standard deviation of the sample means, for each

sample consisting the English scores of 40 randomly selected applicants?

(c)What is the probability that the mean English score in a simple random sample of 40 applicants is above 625 marks?

Need help!!!

### 1 個解答

• 最愛解答

1(a) P(X >= a) = 0.15P[(X - 610)/50 >= (a - 610)/50] = 0.15(a - 610)/50 = 1.0364a = 661.82P(X >= b) = 0.4P[(X - 610)/50 >= (b - 610)/50] = 0.4(b - 610)/50 = 0.2533b = 622.665So, the minimium criteria to get A and B are 661.82 and 622.665 marks respectively(b) Mean = 610 and standard deviation = 50/√40 = 7.9057(c) P(X > 625) = P[(X - 625)/7.9057 > (625 - 610)/7.9057] = P(Z > 1.89736519)=0.02889