The required probability that the sample mean courtship time is between 115 min and 135 min is 0.5269.
We know that probability is defined as the proportion of number of favorable outcomes to the total number of outcomes.
Probability implies plausibility. A piece of math deals with the occasion of a sporadic event. The worth is communicated from zero to one. Likelihood has been acquainted in Maths with foresee how likely occasions are to occur.
The significance of likelihood is essentially the degree to which something is probably going to occur. This is the fundamental likelihood hypothesis, which is likewise utilized in the likelihood dispersion, where you will get familiar with the chance of results for an irregular examination. To track down the likelihood of a solitary occasion to happen, first, we ought to know the complete number of potential results.
We have μ=115min
n=50
P(x₁<X<x₂)=P(z₂< (x₂-μ) /S.D) -P(z₁<(x₂-μ)/S.D)
S.D=√(σ²/ n)
=>S.D=√(115)²/50
=>S.D = √(13225)/50
=>S.D = √264.5
=>S.D = 16.26
P(115<X<135)=P(z₂< (135-115)/16.26)-P(z₁ <(100-115) / 16.26)
=>P((115<X<135)=P(z₂<20/16.26)-P(z₁< -15/16.26)
=>P(115<X<135)=P(z₂<1.23) - P(z₁<-0.922)
From the probability distribution table
P(z₂<1.23)=0.6255
P(z₁<-0.922)=0.0986
P(115<X<135)=0.6255-0.0986
=>P(115<X<135)=0.5269
Hence, required probability is 0.5269
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