Statistics

For a normal population with a mean of 10 and a variance 4, the 
P(
X ≥ 10) is ___.

If the random variable of x is normally distributed, ____ % of all possible observed values of x will be within two standard deviations of the mean.

If the scores on an aptitude test are normally distributed with mean 500 and standard deviation 100, what proportion of the test scores are less than 585?

What is the probability that a random variable having a standard normal distribution is between .87 and 1.28?

The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours. What is the probability that the drone will fly:

Less than 4.66 hours?

The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours. What is the probability that the drone will fly:

Between 4.70 and 4.82 hours?

The weight of a product is normally distributed with a mean of four ounces and a variance of .25 “squared ounces.” What is the probability that a randomly selected unit from a recently manufactured batch weighs no more than 3.5 ounces?

The weight of a product is normally distributed with a mean of four ounces and a variance of .25 “squared ounces.” What is the probability that a randomly selected unit from a recently manufactured batch weighs more than 3.75 ounces?

(Percentile) During the past six months, 73.2% of US households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. 99% of the households spent less than what amount?

(Percentile) During the past six months, 73.2% of US households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. 80% of the households spent more than what amount?

(Percentile) Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be 
normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. Complete the following statement: Only 20% of the individuals wait less than _____ minutes.

(Percentile) Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be 
normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. Suppose that in an effort to provide better service to the public, the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time. The director decides that 15% of the customers should receive this discount. What are the numbers of minutes they need to wait to receive the discount?

Percentile) A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9.

Only 5% of the students taking the test scored higher than what grade?

(Percentile) The yearly cost of dental claims for the employees of the local shoe manufacturing company is normally distributed with a mean of $105 and a standard deviation of $35. What is the yearly cost at which 35% of the employees fall at or below?

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. What percentage of the time will the number of boxes received weekly be between 180 and 210?