Question

The amount of syrup that people put on their pancakes is normally distributed with mean 64 mL and standard deviation 11 mL. Suppose that 47 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

What is the distribution of X? X ~ N

What is the distribution of ¯x? ¯x ~ N

If a single randomly selected individual is observed, find the probability that this person consumes is between 62 mL and 64 mL

For the group of 47 pancake eaters, find the probability that the average amount of syrup is between 62 mL and 64 mL.

For part d), is the assumption that the distribution is normal necessary? yes or no

Answer 1

Solution :

Given that ,

mean = = 64

standard deviation = = 11

a.

X N (64 , 11)

b.

n = 47

= 64

= / n = 11 / 47 = 1.6045

N (64 , 1.6045)

c.

P(62 < x < 64) = P[(62 - 64)/ 11) < (x - ) /  < (64 - 64) / 11) ]

= P(-0.18 < z < 0)

= P(z < 0) - P(z < -0.18)

= 0.5 - 0.4286

= 0.0714

Probablity = 0.0714

d.

= P[(62 - 64) /1.6045 < ( - ) / < (64 - 64) / 1.6045)]

= P(-1.25 < Z < 0)

= P(Z < 0) - P(Z < -1.25)

= 0.5 - 0.1056

= 0.3944

Probability = 0.3944

e.

yes