Question 1205463
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mu = mean = 7.1
sigma = standard deviation = unknown
x = number of days to germinate


"<font color=blue>exactly 70% of the cauliflower seeds germinate in 6.1 days or more</font>" translates to the notation {{{P(x >= 6.1) = 0.70}}}
It's practically the same as {{{P(x > 6.1) = 0.70}}} since the boundary doesn't affect the probability.
The diagram for it will have shading to the right of x = 6.1 underneath the curve. This shaded region has an area of 0.70


We need to find the value of k such that P(z > k) = 0.70
It is equivalent to P(z < k) = 0.30
Note that I'm using z instead of x at this point.


You'll need to use a stats calculator to find the value of k.
You could use a Z table, but it would be fairly inaccurate.


If you have a TI84 calculator or similar then type in:
<font color=blue>invNorm(0.30)</font>
The approximate result is -0.5244005
To reach the invNorm function, press the button labeled "2ND" and then press the VARS key.


Many similar calculators can be used as an alternative. Search out "inverse normal calculator". 
One result that shows up is
https://onlinestatbook.com/2/calculators/inverse_normal_dist.html
It's from professor David M Lane. The calculator is fairly user friendly and offers a diagram as well. 
Two offline alternative routes are the <a href="https://wiki.geogebra.org/en/InverseNormal_Command">InverseNormal command in GeoGebra</a> or <a href="https://support.microsoft.com/en-us/office/norminv-function-87981ab8-2de0-4cb0-b1aa-e21d4cb879b8">normInv command on a spreadsheet</a>


Anyways, we found that k = -0.5244005 approximately
It indicates P(z < -0.5244005) = 0.30
The area under the standard normal curve to the left of z = -0.5244005 is 0.30
30% of the area under the z curve is to the left of that z score.
70% of the area is to the right of that z score.


The raw score that pairs up with that z value is x = 6.1


The last set of steps look like this:
z = (x - mu)/sigma
z*sigma = x - mu
sigma = (x - mu)/z
sigma = (6.1 - 7.1)/(-0.5244005)
sigma = 1.9069394
sigma = <font color=red>1.91</font> when rounding to two decimal places.
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