According to a recent study, the carapace length for adult males of a certain sp

Question

According to a recent study, the carapace length for adult males of a certain species of tarantula are normally distributed with a mean of mu = 17.09 mm and a standard deviation of sigma = 166 mm. Complete parts (a) through (d) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. a. Find the percentage of the tarantulas that have a carapace length between 15 mm and 16 mm. The percentage of the tarantulas that have a carapace length between 15 and 16 is %. (Type an integer or decimal rounded to two decimal places as needed.)

Explanation / Answer

a.

Here mean=17.09 and sd=1.66

Now we need to find P(15<x<16)

As it is given distribution is normal we will convert x to z

Z=x-mu/sd

So P(15-17.09/1.66<z<16-17.09/1.66)=P(-1.26<z<-0.66)=P(0<z<-0.66)-(0<z<-1.26)=-0.2454+0.3962=0.1508

So answer is 15.08%

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