Question

Question 1 of 15 Step 1 of 1 01:05:25 A soft drink machine outputs a mean of 29 ounces per cup. The machine's output is normally distributed with a standard deviation of 4 ounces. What is the probability of filing a cup between 25 and 31 ounces? Round your answer to four decimal places

Answer 1

Since the distribution is normal, hence using Z statistic probability can be calculated

Z value at 25

$Z=\frac{X-\mu}{\sigma}=\frac{25-29}{4}=-1$

And Z at 31

$Z=\frac{X-\mu}{\sigma}=\frac{31-29}{4}=0.5$

Now the probability between 25 and 31 is calculated using Z pvalue table.

P value at Z =0.5 , P(X<31)=P(Z<0.5)

= 0.6915

And probability at Z

x= 25 or P(Z<-1)

=0.1587

hence P( 25<X<31)= 0.6915-0.1587

= 0.5328

Z table as