The United States Census Bureau determined that the mean number of children in an American household is 1.86. Suppose 50 households are polled and the sample mean is found to be 2.1 and the standard deviation is found to be 1.57.

Write a program that finds the probability that another 50 household sample will have a sample mean of at least 2.1.

The output should be:

The probability that another 50 household sample will have a sample mean of at least 2.1 is 0.14251039487167508.

from scipy.stats import t import math

#mean number of children = 1.86 #50 houses are polled and the mean is found to be 1.57 and sd = 1.57 #Therefore we have the following xbar = 2.1 mu = 1.86 sd = 1.57 n = 50 df = n-1 #Degrees of freedom

#find the t statistic t_score = (xbar - mu)/(sd/math.sqrt(n))

probability = t.sf(t_score,df)

print(f"The probability that another 50 household sample will have a sample mean of at least 2.1 is {probability}")