The average rainfall during the month of April follows a normal distribution with a mean of...

The average rainfall during the month of April follows a normal distribution with a mean of 5 in. and a standard deviation of 0.6 in. What is the probability that the rainfall in April will be less than 4 in.?

Solutions

Expert Solution

ANSWER:

Given that,

Mean = = 5 in.

Standard deviation = = 0.6 in

We know that,

z = (x-) / = (x-5) / 0.6

What is the probability that the rainfall in April will be less than 4 in.

P(x < 4) = P((x-) / < (4-5) /0.6)

P(x < 4) = P(z < -1 /0.6)

P(x < 4) = P(z < -1.67)

P(x < 4) = 0.04746 (from z score table)

The probability that the rainfall in April will be less than 4 in. is 0.04746

---------------------------------------------------------------------The End ------------------------------------------------------------------------

If you have any doubt please ask me friend and if you are satisfied with my solution please give me thumb up.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

The annual rainfall in a region has a normal distribution with a mean rainfall of 50...

The annual rainfall in a region has a normal distribution with a mean rainfall of 50 inches and a standard deviation of 10 inches. what is the probability that the total rainfall of four randomly picked years will exceed 220 inches?

The average MCAT score follows a Normal distribution, with a mean of μ = 508 and...

The average MCAT score follows a Normal distribution, with a mean of μ = 508 and a standard deviation of σ = 8. What is the probability that the mean IQ score of 100 randomly selected people will be more than 510?

The diameter of a cylinder follows a normal distribution with the mean of 10cm and the...

The diameter of a cylinder follows a normal distribution with the mean of 10cm and the variance of 0.04 cm^2. a) Construct a Shewhart chart to monitor the process mean of cylinder diameter with a sample size 9? (Use L=3) b) If the mean of the process changes to 10.5 cm, what is the probability that you detect this mean shift at the immediate next sample (the first sample after the mean shift)? c) Continue b), what is the probability...

Assume the distribution of home selling prices follows a normal distribution. for this area the mean...

Assume the distribution of home selling prices follows a normal distribution. for this area the mean selling price is $95,140 and the standard deviation of the selling price is $13,100. Let S be the home selling price. For a randomly selected home find P(S>$100,000). The answer is approx. = .6447. I just really need to know how to set this question up in a TI-84 calculator PLEASE! It's urgent!

The grade of statistics follows a normal distribution with a mean of 85 and a standard...

The grade of statistics follows a normal distribution with a mean of 85 and a standard deviation of 10. The instructor adopted a new teaching method this year, and would like to investigate whether there is an improvement in students’ average grade. Suppose the average grade from a sample of 36 students is 88, can we conclude that there is an improvement at the 5% significance level? A. Specify the null and alternative hypotheses. B. Determine the rejection region. C....

The height of females in the United States follows a normal distribution with a mean of...

The height of females in the United States follows a normal distribution with a mean of 65 inches and a standard deviation of 2 inches. What height marks the median?

There is a river whose average daily flow Q follows a normal distribution. The average flow...

There is a river whose average daily flow Q follows a normal distribution. The average flow is 800 cfs and the standard deviation is 1000 cfs. Determine the following: (a) The probability that the flow observed on a given day exceeds 10,000 cfs. (b) The probability that the observed flow is between 5,000 and 7,000 cfs. c) The value of the flow that has a 1% probability of exceeding.

There is a river whose average daily flow Q follows a normal distribution. The average flow...

There is a river whose average daily flow Q follows a normal distribution. The average flow is 8000 cfs and the standard deviation is 1000 cfs. Determine the following: (a) The probability that the flow observed on a given day exceeds 10,000 cfs. (b) The probability that the observed flow is between 5,000 and 7,000 cfs. (c) The value of the flow that has a 1% probability of exceeding.

Assume the length X of a certain unit follows the normal distribution with a mean of...

Assume the length X of a certain unit follows the normal distribution with a mean of 50mm and a standard deviation of 5 mm. If a random sample of 21 units is taken, find the value C such that Probability(sample variance > C) = 0.90

assuming the length X of a certain unit follows the normal distribution with a mean of...

assuming the length X of a certain unit follows the normal distribution with a mean of 50mm and a standard deviation of 5mm. if a random sample of 21units is taken, find the value C such that probability (sample variance > C)= 0.90

Subjects