I\'m having trouble with the second portion of the question. If anyone could pos

Question

I'm having trouble with the second portion of the question. If anyone could possibly tell me how to figure this out with statcrunch or manually, I would appreciate it

Assume that the readings on the thermometers are normally distributed with a mean of 0 and standard deviation of 1.00°C A thermometer is randomly selected and tested raw a sketch and find the temperature reading corresponding to P84 the 4th percenti e This is the temperature reading separating the bottom 84% om the top 16% Which graph represents Pa4? Choose the correct graph helow D. The temperature for P84 is approximately Round to two decimal places as neaded ) Enter your answer in the answer hox and then click Check Answer All parts showing

Explanation / Answer

Here X is the reading on thermometer. So X~N(0,1002)

Let p be the 84th percentile, i.e P84 = p . (Now percentile means dividing the region into 100 parts)

For the graph, the answer will be D as it show approximately 84% of the region i.e the probabilty where P(X<p)=0.84

From the Biometrica table we can get that 0.8413 is the approx Z-value of 1.00. (Z represents standard normal variable, Z~N(0,1) ) .So, P[z<1.00]= 0.8413

So,

P(X<p) =0.84

=> P[(X/100)<(p/100)]= P[z<1.00] (Standardizing X )

=> P[z<(p/100)]= P[z<1.00] ( In general Z=(X-mean)/S.D )

hence, p/100= 1.00

=> p=100

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