Question

Suppose that the national average for the math portion of the College Board's SAT is 515. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places. If your answer is negative use “minus sign”.

(a) |
What percentage of students have an SAT math score greater than 615? |

(b) |
What percentage of students have an SAT math score greater than 715? |

(c) |
What percentage of students have an SAT math score between 415 and 515? |

(d) |
What is the z-score for student with an SAT math score of 620? |

(e) |
What is the z-score for a student with an SAT math score of 405? |

Please show work. Can this be done using excel?

Answer #1

(since we need to use empirical rule: for which 68%,95% and 99.7% values are within 1,2,3 standard deviaiton from mean , we should not use excel as it will give exact value)

for normal distribution z score =(X-μ)/σx | |

here mean= μ= | 515 |

std deviation =σ= | 100.000 |

a)

probability
=P(X>615)=P(Z>(615-515)/100)=P(Z>1)=1-P(Z<1)=1-0.84
=0.16 ~ 16 % |

b)

probability
=P(X>715)=P(Z>(715-515)/100)=P(Z>2)=1-P(Z<2)=1-0.975
=0.025 ~ 2.5% |

c)

probability
=P(415<X<515)=P((415-515)/100)<Z<(515-515)/100)=P(-1<Z<0)=0.5-0.16=0.34
~ 34% |

d)

z score =(620-515)/100=1.05

e)

z score =(405-515)/100=-1.1

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