Suppose that Xhas a normal distribution, Find E[ekx].

how to Calculate the normal time for each element.

Assume a distribution with mean of 50 and a standard devivation of 12. For an x-value of 65, the z-score is  . (two-decimal accuracy) For a z-score of -2.3, x =  . (one-decimal accuracy)

Find the value of za/2 when 1- a = .98. Explain your answer by using the standard normal curve.

The noon-day temperature (in °C) in Ajax last winter can be represented by the normal distribution X~N( 6, 62). How often was it above - 3°C at noon in Ajax last winter? Make a sketch.

The time spent​ (in days) waiting for a heart transplant in two states for patients with type A+ blood can be approximated by a normal​ distribution, as shown in the graph to the right. Complete parts​ (a) and​ (b) below. u= 134 0=18.1 What is the shortest time spent waiting for a heart that would still place a patient in the top 30​% of waiting​ times?

The mean height of 15 to 18-year-old males from Chile from 2009 to 2010 was 170 cm with a standard deviation of 6.28 cm. Male heights are known to follow a normal distribution. Let X = the height of a 15 to 18-year-old male from Chile in 2009 to 2010. Then X ~ N(170, 6.28). Suppose that the height of a 15 to 18-year-old male from Chile from 2009 to 2010 has a z-score of z = –2. What is the male’s height?  (to the nearest hundredths). The z-score (z = –2) tells you that the male’s height is? standard deviations to the  (right or left) of the mean?

Suppose that the average life of a refrigerator before replacement is μ = 15 years with a (68%of data) range from 13 to 17 years. Let x = age at which a refrigerator is replaced. Assumethat x has a distribution that is approximately normal. Find a good approximation for thestandard deviation of x values.