A particular fruit's weights are normally distributed, with a mean of 446 grams and a standard deviation of 17 grams. If a fruit is picked at random then 14% of the time, its weight will be greater than how many grams?

Answer:The weight corresponding to which weight will be larger than 14% of times equals 427.635 grams.Step-by-step explanation:We need to find the value of weight that corresponds to 14% of area under the normal distribution curve It is given that[tex]\overline{X}=446\\\\\sigma =17[/tex]Using standard normal distribution tables we find value of Z corresponding to 14% of the area as -1.080Thus using the standard equation [tex]Z=\frac{X-\overline{X}}{\sigma }\\\\X=\sigma \times Z+\overline{X}\\\\\therefore X=427.635grams[/tex]