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Let X have a binomial distribution with parameters n = 25 and p. Calculate each of the...

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Question

Basic Math

Let X have a binomial distribution with parameters

n = 25

and p. Calculate each of the following probabilitiesusing the normal approximation (with the continuity correction) forthe cases

p = 0.5, 0.6, and 0.8

and compare to the exact binomial probabilities calculateddirectly from the formula for

b(x; n, p).

(Round your answers to four decimal places.)

(a)

P(15 ≤ X ≤ 20)

p

P(15 ≤ X ≤ 20)

P(14.5 ≤ Normal ≤ 20.5)

0.512
0.634
0.856

(b)

P(X ≤ 15)

p

P(X ≤ 15)

P(Normal ≤ 15.5)

0.51011
0.61213
0.81415

(c)

P(20 ≤ X)

p

P(20 ≤ X)

P(19.5 ≤ Normal)

0.51920
0.62122
0.82324

Answer & Explanation Solved by verified expert
3.6 Ratings (562 Votes)
Mean and standard deviation for normal For 05 Mean np 25 05 125 Standard deviation np1p 25 05 05 25 For 06 Mean np 25 06 15 Standard deviation np1p 25 06 04 24495 For 08 Mean np 25 08 20 Standard deviation np1p 25 08 02 2 a using Binomial For 05 Probability between 15 and 20 P15 X 20 PX 20 PX 15 PX 20 PX 14 BINOMDIST20 25 05 1 BINOMDIST14 25 05 1 02117 For 06 Probability between 15 and 20 P15 X 20 PX 20 PX 15 PX 20 PX 14 BINOMDIST20 25 06 1 BINOMDIST14 25 06 1 05763 For 08 Probability    See Answer
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