Please help-- in a hurry and would really appreciate it!! Thanks in advance :) F

Question

Please help-- in a hurry and would really appreciate it!!
Thanks in advance :)

For this problem, you must use Excel to perform the necessary calculations. Below are the formulas and equations you will need to use. Click on the image below to download a power point version if the text is blurry or too small. If it is appropriate to use the binomial distribution, use the formula binom.dist(number_s,trials,probability,cumulative) to calculate the probability. In this formula, number_s is the number of successful trials, trials is the total number of trials, probability is the probability for a single trial expressed as a decimal, and cumulative should be set as false This will report the binomial distribution probability for a single outcome. You are tasked with reporting a cumulative probability If it is appropriate to use the normal approximation of the binomial distribution, calculate Z using the correct equation from the option below and then use either the formula(1-(norm.dist(Z,0,1,TRUE))) when calculating a probability >Z or the formula-(norm.dist(Z,0,1,TRUE)) for the probabity or PrX Observed] Pr Z

Explanation / Answer

From the information 53% of the flowers of the rewardless orchid are yellow and remaining flowers are purple.

percentage of purple flower =47%

i) P ( Selected flower would it be purple) = 1 -0.53 = 0.47

ii) n = number of flowers selected for sample = 6

X = number of flowers would be purple.

p = probability of flower would it be purple = 0.53

Hence the distribution of random variable X is binomial with n =6 and p =0.47

P ( At least 4 would be purple) = P( X >= 4) = 1- P( X <=3)

P( X<=3) which is cumulative probability at X=3.

by using excel BIN0MDIST(number_s,trials,probability_s,cumulative)

P( X <=3) = BINOMDIST(3,6,0.47,1) = 0.710684

P ( At least 4 would be purple) = P( X >= 4) = 1- 0.710684 = 0.289316

iii) number of trials = n = 260

P(150 or more of the orchid are purple) = P( X >=150) = P( X <= 149)

since number of trials are large . By using binomial approximation of binomial distribution.

P( X <=149) = P( Z < (149 +1/2 -260*0.47) / sqrt(260*047*0.53))

where Z ~ N(0,1) E(Z) =mean = 0 and S.D(Z) =standard deviation = 1

= P(Z <= 3.3922) which is cumulative probability at Z = 3.3922

By using Excel Function NORMDIST(X ,mean, standard_dev,cumulative)

P(Z <= 3.3922) = NORMDIST(3.3922,0,1,true) = 0.9996

P(150 or more of the orchid are purple) = 0.9996

or

By using normal probability table

P(Z <= 3.3922) = 1 - P( Z >3.3922)

from normal probability table

P( Z >3.3922)=0.0003

P(Z <= 3.3922) = 1-.0003 = 0.9997

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