8/ 80-89 90-99 Eo If a student is selected at random, (a) What is the probabilit

Question

8/ 80-89 90-99 Eo If a student is selected at random, (a) What is the probability that the student's score is between 70 and 89? (b) Draw a probability histogram and probability polygon on the same axes. Use the binomial formula to compute the following. 13. If n = 1 7, p 0.25, and x = 5. calculate the probability. 2 pts 14. A student takes a 9-question multiple-choice test by guessing. Each question has 5 choices. What is the probability that: (2 pts each) Pt1/5 =0. (a) At least 4 guesses are correct? (b) Exactly 4 guesses are correet? © At most 5 guesses are correct

Explanation / Answer

14.

Note that binomcdf is a cumulative density function, for at most x successes. binompdf is for exactly x successes.

a)

Here, the probability of getting it right is p = 1/5 = 0.2.

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    9      
p = the probability of a success =    0.2      
x = our critical value of successes =    4      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   3   ) =    0.914358272

[You can get thus using binomcdf(9, 0.2, 3).]
          
Thus, the probability of at least   4   successes is, getting the complement,  
          
P(at least   4   ) =    0.085641728 [ANSWER]

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b)

You can use binompdf(n, p, x) --> binompdf(9,0.2,4) =
P(4) = 0.066060288 [ANSWER]

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c)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    9      
p = the probability of a success =    0.2      
x = the maximum number of successes =    5      
          
Then the cumulative probability is          

[binompdf(9,0.2,5)]
          
P(at most   5   ) =    0.996933632 [ANSWER]

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