Question

The annual per capita consumption of bottled water was

31.931.9

gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of

31.931.9

and a standard deviation of

1212

gallons.

a. What is the probability that someone consumed more than

3232

gallons of bottled​ water?

b. What is the probability that someone consumed between

2525

and

3535

gallons of bottled​ water?

c. What is the probability that someone consumed less than

2525

gallons of bottled​ water?

d.

99.599.5​%

of people consumed less than how many gallons of bottled​ water?

Answer 1

Solution :

Given that ,

mean = = 31.9

standard deviation = =12

P(x >32 ) = 1 - p( x< 32)

=1- p [(x - ) / < (32-31.9) / 12]

=1- P(z <0.008 )

= 1 - 0.008 = 0.992

probability = 0.9920

b)

P(25< x < 35 ) = P[(25-31.9 )/ 12) < (x - ) /  < (35-31.9 ) /12 ) ]

= P(-0.58 < z < 0.26)

= P(z <0.26 ) - P(z <-0.58 )

Using standard normal table

= 0.6026- 0.281 = 0.3216

Probability = 0.3216

c)

P(x < 25) = P[(x - ) / < (25-31.9) /12 ]

= P(z < -0.58)

= 0.281

probability =0.2810

d)

P(Z < z) = 0.995

z =2.576

Using z-score formula,

x = z * +

x =2.576 *12+ 31.9

x = 62.8

Answer = 62.8 water