72% of all students at a college still need to take another math class. If 34 students are randomly selected, find the probability thata. Exactly 23 of them need to take another math class. b. At most 23 of them need to take another math class. c. At least 22 of them need to take another math class. d. Between 21 and 25 (including 21 and 25) of them need to take another math class. Round all answers to 4 decimal places.

Question
Asked Nov 2, 2019
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72% of all students at a college still need to take another math class. If 34 students are randomly selected, find the probability that

a. Exactly 23 of them need to take another math class. 
b. At most 23 of them need to take another math class. 
c. At least 22 of them need to take another math class. 
d. Between 21 and 25 (including 21 and 25) of them need to take another math class. 

Round all answers to 4 decimal places.

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Expert Answer

Step 1

It is given that the probability of a selected student need to take another math class is 0.72.

The random variable X, number of students need to take another math class follows binomial distribution with p = 0.72 and n = 34.

a).

The probability that exactly 23 students need to take another math class can be obtained by entering the formula “=BINOM.DIST(23,34,0.72,FALSE)” in EXCEL software.

BINOM.DIST(23,34,0.72, FALSE)
E
F
G
0.124136707
help_outline

Image Transcriptionclose

BINOM.DIST(23,34,0.72, FALSE) E F G 0.124136707

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Step 2

b).

The probability that at most 23 students need to take another math class can be obtained by entering the formula “=BINOM.DIST(23,34,0.72,TRUE)” in EXCEL software.

BINOM.DIST(23,34,0.72,TRUE)
E
F
G
0.345379043
help_outline

Image Transcriptionclose

BINOM.DIST(23,34,0.72,TRUE) E F G 0.345379043

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Step 3

c).

The probability that at least 22 students need to take another math class can be obtained by entering the f...

-1-BINOM.DIST(21,34,0.72,TRUE)
E
F
G
0.871285487
help_outline

Image Transcriptionclose

-1-BINOM.DIST(21,34,0.72,TRUE) E F G 0.871285487

fullscreen

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