Question

40 select the correct answer from the drop - down menu. the mean midday temperature recorded in june in a city in south california is 36°c, and the standard deviation is 3°c. the number of days in the month of june is 30. assuming the data is normally distributed, the number of days in june when the midday temperature was between 39°c and 42°c is

Explanation:

Step1: Calculate z - scores

For \(x_1 = 39^{\circ}C\), the z - score \(z_1=\frac{x_1-\mu}{\sigma}\), where \(\mu = 36^{\circ}C\) and \(\sigma = 3^{\circ}C\). So \(z_1=\frac{39 - 36}{3}=1\). For \(x_2 = 42^{\circ}C\), the z - score \(z_2=\frac{x_2-\mu}{\sigma}=\frac{42 - 36}{3}=2\).

Step2: Use the standard normal distribution table

The probability \(P(1<Z<2)\) is \(P(Z < 2)-P(Z < 1)\). From the standard - normal table, \(P(Z < 2)=0.9772\) and \(P(Z < 1)=0.8413\). So \(P(1 < Z < 2)=0.9772-0.8413 = 0.1359\).

Step3: Calculate the number of days

The number of days \(n\) in a 30 - day month is \(n = 30\times P(1<Z<2)\). So \(n=30\times0.1359 = 4.077\approx4\).

Answer:

4