Question

Of my students, 75% report that mathematics is a bit stressful
for them. I choose a group of six students and ask them if math is
stressful. (Calculate to 3 decimal places)

a) What is that probability that exactly 3 of the students say they
are stressed about math?

b) what is the probability that more than 4 students say they are
stressed about math?

c) Create a binomial distribution to show the possibilities.

Answer #1

a)

Here, n = 6, p = 0.75, (1 - p) = 0.25 and x = 3

As per binomial distribution formula P(X = x) = nCx * p^x * (1 -
p)^(n - x)

We need to calculate P(X = 3)

P(X = 3) = 6C3 * 0.75^3 * 0.25^3

P(X = 3) = 0.132

b)

We need to calculate P(X >= 5).

P(X >= 5) = (6C5 * 0.75^5 * 0.25^1) + (6C6 * 0.75^6 *
0.25^0)

P(X >= 5) = 0.356 + 0.178

P(X >= 5) = 0.534

c)

x | formula | value |

0 | 6C0 * 0.75^0 * 0.25^6 | 0 |

1 | 6C1 * 0.75^1 * 0.25^5 | 0.004 |

2 | 6C2 * 0.75^2 * 0.25^4 | 0.033 |

3 | 6C3 * 0.75^3 * 0.25^3 | 0.132 |

4 | 6C4 * 0.75^4 * 0.25^2 | 0.297 |

5 | 6C5 * 0.75^5 * 0.25^1 | 0.356 |

6 | 6C6 * 0.75^6 * 0.25^0 | 0.178 |

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