Question

if x follows normal distribution with mean 100 and variance 120 mode is​

Answer 1

Given : x follows normal distribution with mean 100

and variance = 120

To Find :  Mode

Solution :

x follows normal distribution

Mean = 100

Variance = 12

in Normal distribution : Mean Mode and Median coincide and have same values

so Mode will be same as Mean

Hence Mode = 100    

( there is no relevance of variance here as variance shows only the spread )

Mode will be 100

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Answer 2

Answer:

Here we need to determine the value of Z=  

σ

x−μ

​  

 

Here, μ=Mean=30 and σ=Stand Deviation=4

For, x=30⇒Z=  

4

30−30

​  

=0

For, x=35⇒Z=  

4

35−30

​  

=1.25

⇒P(30<x<35)=P(0<Z<1.25)

⇒P(0<Z<1.25)=P(Z<1.25)−P(Z<0)                         (∵P(a<Z<b)=P(Z<b)−P(Z<a))

From the Normal Distribution table, P(Z<1.25)=0.8944 and P(Z<0)=0.5

⇒P(30<x<35)=0.8944−0.5=0.3944