The College Entrance TOEFL test has a mean m = 437 and a standard deviation s = 76. This August the College will receive a Student Services and Support (SSS) grant from the United States Department of Education. This grant will provide academic support including tutoring and academic counseling to incoming freshmen here at the national campus. The target student are those who come in with weak math and English skills.

- What percent of the students will be between 470 and 530 on the TOEFL test? That
is, find the probability P(470<x<530). Report the probability as a decimal or
percent, your choice.

- If 300 freshmen are admitted, how many freshmen will be served by the SSS grant if we
serve only students who score between 470 and 530 on the TOEFL?

- Using the same information on the mean and standard deviation given above, find the
TOEFL score above which only 10% of the students scored. That is, find P(x >
______) = 0.10.

Statistic | Equations | Excel |
---|---|---|

Mean | = = x P(x) | =AVERAGE(data) |

Sample Standard Deviation | = sx = |
=STDEV(data) |

Population Standard Deviation | = s = |
=STDEVP(data) |

Slope | =SLOPE(y data, x data) | |

Intercept | =INTERCEPT(y data, x data) | |

Correlation | =CORREL(y data, x data) | |

Find a probability from a z value | =NORMSDIST(z) | |

Find a z value from a probability p | =NORMSINV(p) |

Excel calculates the probability from the "far left":