Suppose the maximum temperature T on any day in Brisbane in January follows a normal distribution...

Suppose the maximum temperature T on any day in Brisbane in January follows a normal distribution with expectation 31 ◦C (degrees Celsius) and standard deviation 2 ◦C. Any temperature above 35 ◦C is deemed dangerous for older people. Using a ta- ble of the normal distribution or otherwise, find the probability that the temperature in Brisbane reaches a dangerous level on any day in January.

Suppose the expected temperature increases by an amount δ due to global warming, while the standard deviation remains the same. What is the smallest δ that will lead to a 5-fold increase in the probability from the previous question?

Instead of a table you may use R or Python to compute probabilities and quantiles. In R, use the functions pnorm and qnorm. In Python, you may use norm.cdf and norm.ppf, as in

     from scipy.stats import norm
     p = norm.cdf(2.0)      # probability
     q = norm.ppf(0.97725)  # quantile

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

For a healthy human, a body temperature follows a normal distribution with Mean of 98.2 degrees...

For a healthy human, a body temperature follows a normal distribution with Mean of 98.2 degrees Fahrenheit and Standard Deviation of 0.26 degrees Fahrenheit. For an individual suffering with common cold, the average body temperature is 100.6 degrees Fahrenheit with Standard deviation of 0.54 degrees Fahrenheit. Simulate 10000 healthy and 10000 unhealthy individuals and answer questions 14 to 16. 14. If person A is healthy and person B has a cold, which of the events are the most likely? Pick...

The amount of water consumed each day by a healthy adult follows a normal distribution with...

The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.46 liters.A health campaign promotes the consumption of at least 2.0 liters per day: A sample of 10 adults after the campaign shows the following consumption in liters: 1.78 1.90 1.38 1.60 1.80 1.30 1.56 1.90 1.90 1.68 At the 0.050 significance level, can we conclude that water consumption has increased? Calculate and interpret the p-value. A.) State the null hypothesis...

The amount of water consumed each day by a healthy adult follows a normal distribution with...

The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.32 liters. A health campaign promotes the consumption of at least 2.0 liters per day. A sample of 10 adults after the campaign shows the following consumption in liters: 1.35 1.42 1.34 1.42 1.44 1.64 1.90 1.64 1.50 1.38 At the 0.025 significance level, can we conclude that water consumption has increased? Calculate and interpret the p-value. State the null hypothesis...

The amount of water consumed each day by a healthy adult follows a normal distribution with...

The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.38 liters. A health campaign promotes the consumption of at least 2.0 liters per day. A sample of 10 adults after the campaign shows the following consumption in liters: 1.48 1.50 1.42 1.40 1.56 1.80 1.62 1.84 1.42 1.39 At the 0.050 significance level, can we conclude that water consumption has increased? Calculate and interpret the p-value. State the null hypothesis...

The amount of water consumed each day by a healthy adult follows a normal distribution with...

The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.50 liters. A sample of 10 adults after the campaign shows the following consumption in liters: 1.52 1.64 1.66 1.40 1.82 1.70 1.90 1.45 1.78 1.92 At the .01 significance level, can we conclude that water consumption has increased? Calculate and interpret the p-value. (a) State the null hypothesis and the alternate hypothesis. (Round your answers to 2 decimal places.) H0:...

Suppose time to failure follows normal distribution as, T tilde N open parentheses 2 comma space...

Suppose time to failure follows normal distribution as, T tilde N open parentheses 2 comma space 9 close parentheses. The failure rate function z(2.1) is

Suppose the amount of protein in a serving of 2 eggs follows a normal distribution with...

Suppose the amount of protein in a serving of 2 eggs follows a normal distribution with mean 12 grams and standard deviation 1 gram. Let Y denote the amount of protein in a randomly selected serving of 2 eggs. Determine the following probabilities (enter each as a decimal, and round to 4 decimal places): P(Y>10) P(Y≥10) P(Y<12) P(Y=12)

Suppose that the monthly demand for a consumer good follows a normal distribution with a deviation...

Suppose that the monthly demand for a consumer good follows a normal distribution with a deviation of 94 kg. We know that the probability of monthly demand is below 502 kg. is 0.12. Find the mean of the distribution.

Suppose the weight of a grizzly bear cub follows a Normal distribution with a mean weight...

Suppose the weight of a grizzly bear cub follows a Normal distribution with a mean weight of 650 grams and a standad deviation of 20 grams. i) What is the probability that a newborn grizzly bear cub weighs less than 625 grams? ii) what is the probability that a new born grizzly weighs between 608 and 675 grams? iii) What weight is at the 90th percentile? iv) If we take a random sample of 4 new born grizzly bear cubs...

Suppose the length in cm of a male soccer player's foot follows a Normal distribution with...

Suppose the length in cm of a male soccer player's foot follows a Normal distribution with mean 31 and variance 25. Suppose the length in cm of a female soccer player's foot follows a Normal distribution with mean 26 and variance 16. A male and female soccer player are selected at random. What is the probability the female player has a longer foot than the male player? Question 13 options: 0.05 0.22 0.29 0.78 0.95 Independently of one another, a...

Subjects