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Asked Dec 3, 2019
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If no 25 and nq 25, estimate P(fewer than 7) with n 14
rse
approximation is not suitable.
and
p 0.6 by using the normal distribution as an approximation to the binomial distribution; if np< 5 or nq<5, then state that the normal
Select the correct choice below and, if necessary, fill in the answer box to complete your
ou
choice
O A. P(fewer than 7)=
(Round to four decimal places as needed.)
ign
B. The normal approximation is not suitable.
dy
adel
atCr
Тext
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If no 25 and nq 25, estimate P(fewer than 7) with n 14 rse approximation is not suitable. and p 0.6 by using the normal distribution as an approximation to the binomial distribution; if np< 5 or nq<5, then state that the normal Select the correct choice below and, if necessary, fill in the answer box to complete your ou choice O A. P(fewer than 7)= (Round to four decimal places as needed.) ign B. The normal approximation is not suitable. dy adel atCr Тext Click to select and enter your answer(s) and then click Check Answer hapt Check Answer Clear All All parts showing Tools fo OK 10:30 3 ^# 12/3 e Ot Type here to search

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Expert Answer

Step 1

The binomial distribution can be approximated to normal if np is greater than 5 and nq is also greater than 5.

 

Here,

 

Both np and nq are greater than 5. Thus, the normal distribution as an approximation of binomial can be used.

 

The mean and standard deviation of the normal distribution are,

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L=np 14(0.6) 8.4 Thus, the mean is 8.4 -V14 (0.6)(0.4) -1.83 Thus, the standard deviation is 1.83.

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Step 2

Before calculating the probability, the continuity correction factor is applied. Since, the discrete distribution is approximated to a continuous distribution, a continuity correction factor is used to compute the probability.

 

That is, P(X<7-0.5) =P(X<6.5)

The probability of getting fewer than 7 successes is calculated below:

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P(X <7) = P(X <6.5) – 4 X - u 6.5- 8.4 1.83 = P(Z < -1.04)

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Step 3

The probability value corresponding to the Z-sco...

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f NORM.S.DIST(-1.04,TRUE) D1 E G 0.14917 1

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