Question

A soft drink machine is programmed to dispense an average of 400mL per small cup. Suppose the distribution of the amount of drink dispensed is normall distributed with a standard deviation of 13mL. Suppose a random sample of 100 filled small cups is obtained.

a. What's the probability the average amount of soda dispensed in the 100 small cups is less than 390mL?

b.What's the probability the average amount of soda dispensed in the 100 small cups is between 375mL and 390mL?

Answer 1

olution :

Given that ,

mean = $\mu$ = 400

standard deviation = $\sigma$ = 13

n = 100

(a)

P(x < 390) = P((x - $\mu$ ) / $\sigma$ < (390 - 400) / 13)

= P(z < -0.77)

= 0.2207

Probability = 0.2207

(b)

P(375 < x < 390) = P((375 - 400)/ 13) < (x - $\mu$ ) / $\sigma$ < (390 - 400) / 13) )

= P(-1.92 < z < -0.77)

= P(z < -0.77) - P(z < -1.92)

= 0.2207 - 0.0274

= 0.1933

Probability = 0.1933