Using the Central Limit Theorem Answers

The monthly cost for cell phones for plan Amazing has a mean of $39.17 with a standard deviation of $13.58, while the monthly cost for plan Best has a mean cost of $41.16 with a standard deviation of $7.18. A random sample of 37 phones is selected from plan Amazing, and a random sample of 40 phones is selected from plan Best. What is the probability that the mean cost for plan Amazing will be more than the mean cost for plan Best?

The volume of liquid soap in containers labeled as 7 oz is approximately Normally distributed and has a mean of 7.15 oz and a standard deviation of 0.11 oz. If 8 bottles of the soap are randomly selected, what is the probability that the mean is less than 7.11 oz?

The times a musician spends performing a rock song and a country song are approximately Normally distributed. The rock song has a mean time of 133 seconds with a standard deviation of 3.5 seconds, and the country song has a mean time of 126 seconds with a standard deviation of 3.3 seconds. If the musician randomly selects 4 times the rock song is played and 3 times the country song is played, what is the probability that the mean time for the rock song is less than the mean time for the country song?

The time needed for passengers to board the Twisting Thunder roller coaster is skewed right with a mean of 49 seconds and a standard deviation of 7.1 seconds. The time to board the Spiral Wonder roller coaster is skewed left with a mean of 44.8 seconds and a standard deviation of 3.7 seconds. What is the probability in a random sample of 32 times loading Twisting Thunder and 36 times loading Spiral Wonder that the mean time for Twisting Thunder is less than that of Spiral Wonder?

The cost to produce a batch of granola bars is approximately Normally distributed with a mean of $7.19 and a standard deviation of $0.86. If a random sample of 12 batches of granola bars is selected, what is the probability that the mean cost will be more than $7.00?

The heights of a species of plant are approximately Normally distributed, have a mean of 9.31 cm, and have a standard deviation of 0.55 cm. If 20 of the plants are randomly selected, what is the probability that the mean plant height is less than 9.5 cm?

The number of pieces of cat food in a one-cup scoop is approximately Normally distributed with a mean of 344 pieces and a standard deviation of 16 pieces. If a random sample of 28 scoops of cat food is selected, what is the probability that the mean number of pieces will be more than 350 pieces?

The total number of forks dropped by customers per day at a busy restaurant is multimodal with a mean of 24.5 and a standard deviation of 3.3. If a random sample of 80 days is selected, what is the probability that the mean number of forks dropped during those days will be more than 25?

The distribution of time spent brushing teeth for the 1,200 students in a school is multimodal with a mean of 43 seconds and a standard deviation of 8.99 seconds. If a random sample of 9 students is selected, is it appropriate to calculate the probability of the sample mean being less than 30 seconds using an approximately Normal model?

A course for a snail race has times that are skewed right with a mean of 5.18 minutes and a standard deviation of 2.34 minutes. If a random sample of 38 snails is selected, what is the probability that the mean race time is less than 4.3 minutes?