Question

A quiz for a Psychology class consists of 5 questions. The questions are multiple-choice with 4 possible answers each, with only one correct answer. A student randomly guesses on all 5 questions.

- create a probability distribution for the number of correct answers
- what is the probability that the student will pass with a 60% or better
- what is the probability that the student will answer less than 4 correct

Answer #1

Sample size , n = 5

Probability of an event of interest, p = 0.25

**Binomial Probability Distribution4**

what is the probability that the student will pass with a 60% or better

= P(X>=3)

X | P(X) | |

P ( X = 3) = C (5,3) * 0.25^3 * ( 1 - 0.25)^2= | 3 | 0.0879 |

P ( X = 4) = C (5,4) * 0.25^4 * ( 1 - 0.25)^1= | 4 | 0.0146 |

P ( X = 5) = C (5,5) * 0.25^5 * ( 1 - 0.25)^0= | 5 | 0.0010 |

**= 0.1035**

what is the probability that the student will answer less than 4 correct

= P(X<4)

X | P(X) | |

P ( X = 0) = C (5,0) * 0.25^0 * ( 1 - 0.25)^5= | 0 | 0.2373 |

P ( X = 1) = C (5,1) * 0.25^1 * ( 1 - 0.25)^4= | 1 | 0.3955 |

P ( X = 2) = C (5,2) * 0.25^2 * ( 1 - 0.25)^3= | 2 | 0.2637 |

P ( X = 3) = C (5,3) * 0.25^3 * ( 1 - 0.25)^2= | 3 | 0.0879 |

**=0.9844**

**THANKS**

**revert back for doubt**

**please upvote**

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