Answer :
The average time allowed the 15 selected students to be 3.06hours
What is Average?
In plain English, an average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.
With a sample size of 15 and a p value of 0.04
From binomial probability, (nCx)px(1p) is where the application of binomial probability originates from (n-x)
1 - p = 0.96
a) P(x=1) is the probability that precisely 1 received a special accommodation.
= 15C1 x (0.04)^1 x (0.96) ^14 = 0.3388
b) P(x >=1) = 1 - P(x = 0) is the likelihood that at least 1 person received a special accommodation.
= 1 - [ 15C0 x (0.04)^0 x (0.96)^15 = 0.4579
c) the likelihood that two people at least obtained special accommodations
= [P(x = 0) + P(x = 1)] - [P(x>=2) = P(x>=2)
= 1 - [ 15C0 x (0.04)^0 x (0.96)^15 + 15C1 x (0.04)^1 x (0.96)^14]
= 1 - [0.5420 + 0.3388] .3388]
= 0.1192
d) likelihood that the proportion of the 15 who received a special accommodation is within two standard deviations of the proportion you would anticipate receiving one;
= P( x<=1) = P( x= 0) = 0.5429
e) expected average time = 0.04 x 4.5 + 0.96 x 3 = 3.06hours
Hence, The average time allowed the 15 selected students to be 3.06hours
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